If the P -value is small, say less than (or equal to) α, then it is unlikely. And, if the P -value is large, say more than α, then it is likely. If the P -value is less than (or equal to) α, then the null hypothesis is rejected in favor of the alternative hypothesis If the p-value is less than a in a two-tail test, a) the null hypothesis should not be rejected. b) the null hypothesis should be rejected. c) a one-tail test should be used. d) no conclusion should be reached 2. A major department store chain is interested in estimating the mean amount its credit card customers spent on their first visit to.

The p-value (or the observed level of significance) is the smallest level of significance at which you can reject the null hypothesis, assuming the null hypothesis is true. You can also think about the p-value as the total area of the region of rejection. Remember that in a one-tailed test, the reg So in an upper-tailed test, the value of your test variable (t in the t-test, etc.) might be greater than whatever the value in your lookup table would be, but the value of p that you look up from needs to be less than your chosen value (what you call alpha). Using p < 0.05 is more tradition than anything else - it essentially means that you'll. A two-tailed test will test both if the mean is significantly greater than x and if the mean significantly less than x. The mean is considered significantly different from x if the test statistic is in the top 2.5% or bottom 2.5% of its probability distribution, resulting in a p-value less than 0.05 P value = 2 * P [test statistic > = | observation value of test statistic |] P-value decision making. We compared the p value with the significance level (alpha) to make a decision on the null hypothesis. If P is greater than alpha, we do not reject the null hypothesis. If the value of P is less than alpha, we reject the null hypothesis The p-value and the confidence interval are related and have a consistent interpretation: if the p-value is less than α then a (1-α)*100% confidence interval will not contain zero. For example, if the p-value is less than 0.05 then a 95% confidence interval will not contain zero

* If the p-value is less than alpha in a one-tailed test: a*. alpha should be changed. b.a one-tailed test should be used. c. the null hypothesis should not be rejected. d.the null hypothesis should be rejected The other number that is part of a test of significance is a p-value. A p-value is also a probability, but it comes from a different source than alpha. Every test statistic has a corresponding probability or p-value. This value is the probability that the observed statistic occurred by chance alone, assuming that the null hypothesis is true If the p-value is less than alpha in a one-tail test, what conclusion can you draw? The null hypothesis should not be rejected. The null hypothesis should be rejected. A two-tail test should be used We use a two-tailed test because we care whether the mean is greater than or less than the target value. To interpret the results, simply compare the p-value to your significance level. If the p-value is less than the significance level, you know that the test statistic fell into one of the critical regions, but which one Your comparison of the two mouse diets results in a p -value of less than 0.01, below your alpha value of 0.05; therefore you determine that there is a statistically significant difference between the two diets

p-value indicates how extreme the data are. We compare the p-value with the alpha to determine whether the observed data are statistically significantly different from the null hypothesis: If the . p-value. is less than or equal to the . alpha (p< .05), then we reject the null hypothesis, and we say the result is statistically significant. If. If the p-value is less than alpha—the risk you're willing to take of making a wrong decision—then you reject the null hypothesis. For example, if the p-value was 0.02 (as in the Minitab output below) and we're using an alpha of 0.05, we'd reject the null hypothesis and conclude that the average price of Cairn terrier is NOT $400

- If your P value is less than or equal to your alpha level, reject the null hypothesis. The P value results are consistent with our graphical representation. The P value of 0.03112 is significant at the alpha level of 0.05 but not 0.01. Again, in practice, you pick one significance level before the experiment and stick with it
- Two- and one-tailed tests. The one-tailed test is appropriate when there is a difference between groups in a specific direction [].It is less common than the two-tailed test, so the rest of the article focuses on this one.. 3. Types of t-test. Depending on the assumptions of your distributions, there are different types of statistical tests
- This value 2.89 is called the test statistic. This takes us to our last step. 5. Draw a conclusion. So, if you look at the curve, the value of 2.89 will definitely lie on the red area towards the right of the curve because the critical value of 1.96 is less than 2.89. As the value lies in the rejection region, we could reject the Null hypothesis
- A simple calculator that generates a P Value from a z score. P Value from Z Score Calculator. This is very easy: just stick your Z score in the box marked Z score, select your significance level and whether you're testing a one or two-tailed hypothesis (if you're not sure, go with the defaults), then press the button
- ing the decision rule
- If my p-value, if it is less than Alpha, then I reject my null hypothesis and say that I have evidence for my alternative hypothesis. Now, if we have the other situation, if my p-value is greater than or equal to, in this case 0.05, so if it's greater than or equal to my significance level, then I cannot reject the null hypothesis

If the p -value is less than the chosen significance level (α), that suggests that the observed data is sufficiently inconsistent with the null hypothesis and that the null hypothesis may be rejected. However, that does not prove that the tested hypothesis is false ** If, in a (two-tail) hypothesis test, the p-value is 0**.0308, what is your statistical decision if you test the null hypothesis at the 0.08 level of significance? choose the correct answer below? Since the p-value is less than alpha, do not reject H_0. Since the p-value is greater than alpha, do not reject H_0

If the alternate hypothesis gives the alternate in both directions (less than and greater than) of the value of the parameter specified in the null hypothesis, it is called a Two-tailed test. If the alternate hypothesis gives the alternate in only one direction (either less than or greater than) of the value of the parameter specified in the. Often in statistics, a hypothesis test will result in a t-score test statistic. Once we find this t-score, we typically find the p-value associated with it. If this p-value is less than a certain alpha level (e.g. 0.10, 0.05, 0.01), then we reject the null hypothesis of the test and conclude that our findings are significant If the p-value is less than the pre-specified alpha level (usually.05 or.01) we will conclude that mean is statistically significantly different from zero. For example, the p-value is smaller than 0.05. So we conclude that the mean for write is different from 50 **P-value** ≤ α: The difference between the means is statistically significant (Reject H 0) If the **p-value** **is** **less** **than** or equal to the significance level, the decision is to reject the null hypothesis. You can conclude that the difference between the population means is statistically significant

- If the p-value is less than alpha in a two-tailed test, o the null hypothesis should not be rejected. o the null hypothesis should be rejected. O a on-tailed test should be used. O no conclusion should be reached
- Answer to: If the p-value = 0.0684, alpha = 0.10, and it is a two-tailed test, state whether or not the null hypothesis should be rejected
- If the p-value is less than alpha in a one-tailed test: the null hypothesis should be rejected. alpha should be changed. a one-tailed test should be used. the null hypothesis should not be rejected. If a one-tailed test for a proportion is being performed and the upper critical value is +2.33 and the test statistic is equal to +1.37, then
- If the p-value is very small, then either the null hypothesis is false or something unlikely has occurred. In a formal significance test, the null hypothesis is rejected if the p-value is less than a pre-defined threshold value , which is referred to as the alpha level or significance level
- A two-tailed test is the statistical testing of whether a distribution is two-sided and if a sample is greater than or less than a range of values
- The calculator will find the p-value for two-tailed, right-tailed and left-tailed tests from normal, Student's (T-distribution), chi-squared and Fisher (F-distribution) distributions. Show Instructions. In general, you can skip the multiplication sign, so `5x` is equivalent to `5*x`

Recall that if the p-value is less than alpha in a one-tailed test, this means that the observed statistic lies in the rejection region. The name rejection refers to the rejection of the null hypothesis. So if the p-value is less than alpha in a one-tailed test, then the null hypothesis should be rejected. So the answer is C The most common threshold is p < 0.05, which means that the data is likely to occur less than 5% of the time under the null hypothesis. When the p-value falls below the chosen alpha value, then we say the result of the test is statistically significant Things to Know About the p-Value. Here are some useful tips regarding p-value calculations in Excel. If the p-value is equal to 0.05 (5%), the data in your table is significant. If it is less than. •Other software programs will give you the p-value •Just remember the following •Decide if it is a one-or two tailed test and calculate the p-value for your test statistic •Compare the p-value to your level of alpha •If p is less than alpha, you can reject the Null Hypothesis 10 Let's revisit the Systolic BP for patients with BMI > 3 If the p-value is less than the alpha value, you can conclude that the difference you observed is statistically significant. P-Value: the probability that the results were due to chance and not based on your program. P-values range from 0 to 1. The lower the p-value, the more likely it is that a difference occurred as a result of your program

- To say that a result is statistically significant at the level alpha just means that the p-value is less than alpha. For instance, for a value of alpha = 0.05, if the p-value is greater than 0.05, then we fail to reject the null hypothesis. There are some instances in which we would need a very small p-value to reject a null hypothesis
- If the p-value is less than α, then this represents a statistically significant p-value. This means that we can reject the claimed hypothesis. If the p-value is greater than or equal to α, we cannot reject the claimed hypothesis
- A two-tailed test is the statistical testing of whether a distribution is two-sided and if a sample is greater than or less than a range of values. more Statistical Significance Definitio
- If the p-value is greater than alpha, you assume that the null hypothesis is true. If the p-value is less than alpha, you assume that null hypothesis is false. What do you do if the two values are very close? For example, maybe the p-value is 0.06 and alpha is 0.05
- Before you do any hypothesis testing you should decide on your null hypothesis and enumerate the alternative or alternatives. For example, if you have an existing drug A and a proposed new drug B your null will be that there is no difference betwe..
- Most commonly, an alpha value of 0.05 is used, but there is nothing magic about this value. If the p -value for the test is less than alpha, we reject the null hypothesis. If the p -value is greater than or equal to alpha, we fail to reject the null hypothesis
- The sum of positive signs will obviously be the smaller sum, namely 3.5= T.From Table VIII, the p-value for n= 9 with T= 3.5 for a two-tailed test lies between 0.020 and 0.027, about .024.Because he chose a one-tailed test, the tabulated value may be halved, or p= 0.012, approximately, clearly significant.He concludes that the patients' average functionality is significantly below 90%

In the case of a two-tailed z-test, more extreme means having a z-value at least as great in magnitude (at least as far from zero) as the observed z-value. So if your sample gives a z-value of say 1.3 (just for an example), then the p-value will be the area to the right of 1.3 plus the area to the left of -1.3 * The level of statistical significance is often expressed as a p-value between 0 and 1*. The smaller the p-value, the stronger the evidence that you should reject the null hypothesis. A p-value less than 0.05 (typically ≤ 0.05) is statistically significant. It indicates strong evidence against the null hypothesis, as there is less than a 5%. how to find p-value in statistical hypothesis testing. p-value of the test is probability that the test statistic under null hypothesis.p value to z scor Since the \(p\text{-value}\), \(p = 0.00063\), is less than the alpha level of 0.01, the sample data indicates that we should reject the null hypothesis. In conclusion, the sample data support the claim that the proportion of sexual assaults in Daviess County, Kentucky is different from the national average proportion

Here, the t Stat is negative, so the one-tail p-value is for the left tail test, which is what we need. It is 0.033 which is less than our alpha of 0.05. So, this result also tells us to reject the Null and we conclude the Obesity Prevalence in Montgomery County is significantly less than the Mean Obesity Prevalence of the other Alabama counties A smaller alpha value suggests a more robust interpretation of the null hypothesis, such as 1% or 0.1%. The hypothesis test returns a probability value known as p-value. Using this value we can.. P values less than 0.0001 shown as < .0001. P values less than 0.001 are summarized with three asterisks, and P values less than 0.0001 are summarized with four asterisks. Choose how many digits you want to see after the decimal point, up to 15. P values less than 0.001 are given three asterisks, and P values less than 0.0001 are given four. The basic answer to your question is Yes, if you specify an Alpha risk of 0.1 then if the p-value is greater than 0.10 you would accept the null and conclude that there is insufficient evidence to show a difference, and conversely if the value were < 0.1 you would reject the null If the null hypothesis is right, then the distribution of the p-value is Uniform on $[0,1]$. That means that we have exactly an $\alpha$ chance to be wrong in acepting the null hypothesis. Answering your original question: Your reasoning is not right. We accepted the null hypothesis because the p-value was greater than $\alpha$

In statistical significance testing, a one-tailed test and a two-tailed test are alternative ways of computing the statistical significance of a parameter inferred from a data set, in terms of a test statistic.A two-tailed test is appropriate if the estimated value is greater or less than a certain range of values, for example, whether a test taker may score above or below a specific range of. In simple terms, the p-value tells us how inline the sample set is with the null hypothesis. Hence, a large p-value tells us that that the sample set is more inline with the null hypothesis, and. p-values are the probability of procuring an effect no less than as intense as the one in the test data, assuming the null hypothesis to be true. For example, the significant value at 7% signifies that the p-values are less than 0.07 or p < 0.07. Correspondingly, when a result is significant at 2%, it means that p < 0.01 To test the assumption of normality, we can use the Shapiro-Wilks test. From this test, the Sig. (p) value is compared to the a priori alpha level (level of significance for the statistic) - and a determination is made as to reject (p < a) or retain (p > a) the null hypothesis. Tests of Normality.229 15 .033 .917 15 .170.209 15 .076 .888 15 .06

To calculate the correct P value, you need to divide the output P-value by 2. Apply the following logic if you are performing a one tailed test: For greater than test: Reject H0 if p/2 < alpha (0.05). In this case, t will be greater than 0. For lesser than test: Reject H0 if p/2 < alpha (0.05). In this case, t will be less than 0 A two-tailed test is appropriate if the estimated value may be more than or less than the reference value, for example, whether a test taker may score above or below the historical average. A one-tailed test is appropriate if the estimated value may depart from the reference value in only one direction , for example, whether a machine. For any test (directional or non-directional), We reject the null hypothesis if the p-value is less than or equal to the level of significance. Answer and Explanation: 1 a * In this example, the t value is 0*.377 (you can ignore the sign.) The column labeled df gives the degrees of freedom associated with the t

test value z sn µ µ α µ = ≠ = = = = =± − − = = = Do not reject the null hypothesis. There is enough evidence to reject the claim that the average height differs from 29 inches. 15) State whether the null hypothesis should be rejected on the basis of the given P-value. a) P-value= 0.258, α=0.05, one tailed test. If P-value . ≤α. Note that for these two tailed tests we are using the absolute value of the z-score. Because .0188 < .05, we reject the hypothesis (which we shall call the null hypothesis) at the 5% significance level; if the null hypothesis were true, we would get such a large z-score less than 5% of the time For a significance level of 0.05 and 19 degrees of freedom, the critical value for the t-test is 2.093. Since the absolute value of our test statistic (6.70) is greater than the critical value (2.093) we reject the null hypothesis and conclude that there is on average a non-zero change in cholesterol from 1952 to 1962 High School Stats Chapter 9 Section

The results of a lower-tailed test are always opposite the results of a two-tailed test, so we would fail to reject the null hypothesis. The conclusion would be the same as the two-tailed test. Although the P-value for the lower-tailed test is different, it is still less than alpha. The conclusion would be the same as the two-tailed test Significance Levels The significance level for a given hypothesis test is a value for which a P-value less than or equal to is considered statistically significant. Typical values for are 0.1, 0.05, and 0.01. These values correspond to the probability of observing such an extreme value by chance. In the test score example above, the P-value is 0.0082, so the probability of observing such a. If the p-value is less than {eq}\alpha {/eq} in a two-tail test: A. the null hypothesis should be rejected B. the null hypothesis should not be rejecte

In a two-tailed test, there are two rejections regions also known as critical regions, one on each tail of the curve. For a 5% significance level, the value of alpha (α) is 0.05. it defines the probability of the rejection area for the null hypothesis when it is true two-tailed Student's t-test; t = 1.95; p-value = 0.076; Check student's solution. Alpha: 0.05; Decision: Reject the null hypothesis. Reason for decision: The p-value is greater than 0.05; Conclusion: There is insufficient evidence to conclude that the average IQ of brown trout is not four. (3.8865,5.9468 Introduction to P-Value in Regression. P-Value is defined as the most important step to accept or reject a null hypothesis. Since it tests the null hypothesis that its coefficient turns out to be zero i.e. for a lower value of the p-value (<0.05) the null hypothesis can be rejected otherwise null hypothesis will hold

- Here's our problem statement: The test statistic of z = 1.25 is obtained when testing the claim that p does not equal 0.2978. A: Identify the hypothesis test as being two-tailed, left tailed, or right tailed. B: Find the P-value. C: Using a significance level of alpha equals 10%, should we reject H-naught, or should we fail to reject H-naught
- I understand that two-tailed p-values above 0.03822 could be related to possible bias. Therefore, the p-value less than 0.05 implicates publication bias. Upper Bound for p-Value of the.
- e whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed. A)right-tailed B)left-tailed C)two-tailed 4
- Its p-value is less than 0.001. The p-value 0.001 means if you sample 1000 different groups, you'd see the same statistics (or more extreme cases) only 1 time, given anorexia and ICU are indeed independent. 4. What P-value is NOT about. The p-value is often misunderstood as being the probability that the null hypothesis is true
- If the p-value is LESS THAN the significance level $\alpha$ we can report: the sample provides statistically significant evidence that the claim is true, or; the result of the study is statistically significant. Result. Since the (p-value = .1672898) > ($\alpha = .05$

) = P-value, (<) P(z < z o) = P-value, Two Tailed ( ): 2P(z > z o ) = P-value Therefore, if the P-value is less than the significance level you would reject the null hypothesis and if the P-value is greater than the significance level you would accept the null hypothesis. The P-value Approach - Use when you are given a Minitab Printou Because TINV gives the cutoff for a two-tailed t-test, use 2*Alpha instead of Alpha. If the two-tailed probability of a t value higher in absolute value than this cutoff is 0.10, the one-tailed probability of a t value higher than this cutoff is 0.05 (as is the one-tailed probability of a t value less than the negative of this cutoff) As a result, it provides so-called p-values as a final result of a test. P-value is the probability of rejecting the null hypothesis when H0 is true. If the P-value is less than the significance level (usually 0.05), than we say the result is significant

a) In a two-tailed test the critical value for 0.05 level of significance is -1.960 and 1.960: Note in a two-tailed test we divide the significance level by 2 and use the result(in this case 0.025) as the probability to look up the critical z-value As such, in this example where p = .03, we would reject the null hypothesis and accept the alternative hypothesis. We reject it because at a significance level of 0.03 (i.e., less than a 5% chance), the result we obtained could happen too frequently for us to be confident that it was the two teaching methods that had an effect on exam performance In this example, the significance (p value) of Levene's test is .880. If this value is less than or equal to 5% level of significance (.05), then you can reject the null hypothesis that the variability of the two groups is equal, implying that the variances are unequal The standardizing formula can not be solved as it is because we do not have μ, the population mean. However, if we substitute in the hypothesized value of the mean, μ 0 in the formula as above, we can compute a Z value. This is the test statistic for a test of hypothesis for a mean and is presented in .We interpret this Z value as the associated probability that a sample with a sample mean. For practical purposes, reject a null hypothesis if the p-value is less than alpha (generally 5% or 0.05) T-test: The t-test is used to find out if the means between two populations is significantly different. Characteristics of the test are; 1) The test statistic follows a t distribution under null hypothesis

Two-Tailed Test. A two-tailed test has two critical values, one on each side of the distribution, which is often assumed to be symmetrical (e.g. Gaussian and Student-t distributions.). When using a two-tailed test, a significance level (or alpha) used in the calculation of the critical values must be divided by 2 In this video, we review how to correctly interpret and report the results of a statistical test using an alpha of .05.Click here for free access to all of o.. Since the p-value, p = 0.00063, is less than the alpha level of 0.01, the sample data indicates that we should reject the null hypothesis. In conclusion, the sample data support the claim that the proportion of sexual assaults in Daviess County, Kentucky is different from the national average proportion The p-value is the area to the right or left of the test statistic. If it is a two tail test, then look up the probability in one tail and double it. If the test statistic is in the critical region, then the p-value will be less than the level of significance. It does not matter whether it is a left tail, right tail, or two tail test. This rule.

Z-score to P-value Calculator. Use this Z to P calculator to easily convert Z-scores to P-values (one or two-tailed) and see if a result is statistically significant. Z-score to percentile calculator with detailed information on p-values, interpretation, and the difference between one-sided and two-sided percentiles The p-value of the test is 7.95310^{-6}, which is less than the significance level alpha = 0.05. We can conclude that the mean weight of the mice is significantly different from 25g with a p-value = 7.95310^{-6} * Similarly, for a large p-value such as 0*.4, as opposed to a p-value of 0.056 (alpha = 0.05 is less than either number), a data analyst should have more confidence that she made the correct decision in not rejecting the null hypothesis. This makes the data analyst use judgment rather than mindlessly applying rules

- It goes on to say that scipy always gives the test statistic as signed. This means that given p and t values from a two-tailed test, you would reject the null hypothesis of a greater-than test when p/2 < alpha and t > 0, and of a less-than test when p/2 < alpha and t < 0
- When p-value is less than alpha or equal 0.000, it means that significance, mainly when you choose alternative hypotheses, however, while using ANOVA analysis p-value must be greater than Alpha
- Test Statistic: \( T = (N-1)(s/\sigma_0)^2 \) where N is the sample size and s is the sample standard deviation. The key element of this formula is the ratio s/σ 0 which compares the ratio of the sample standard deviation to the target standard deviation. The more this ratio deviates from 1, the more likely we are to reject the null hypothesis
- In this example, the p value for the sign test is .008. Decide whether to reject H 0. If the p value is less than the specified level (.05), we can reject H 0. For the Wilcoxon matched-pairs signed-rank test, the p value was .011 which is less than
- Instead of using the critical value, we apply the pt function to compute the two-tailed p-value of the test statistic. It doubles the lower tail p-value as the sample mean is less than the hypothesized value. Since it turns out to be greater than the .05 significance level, we do not reject the null hypothesis that μ = 15. 4
- Each P value is interpreted individually without regard to the others. You set a value for the significance level, alpha, often set to 0.05. This value serves as a threshold against which the P values are compared. If a P value is less than alpha, that comparison is deemed to be statistically significant
- We evaluate the hypotheses by comparing the p-value to the significance level. Because the p-value is less than the significance level \((p-value = 0.007 < 0.05 = \alpha)\), we reject the null hypothesis. What we observed is so unusual with respect to the null hypothesis that it casts serious doubt on H 0 and provides strong evidence favoring H A

This is a two-tailed test. Distribution for the test: Use t df where df is calculated using the df formula for independent groups, two population means. Using a calculator, df is approximately 18.8462. Do not pool the variances. Calculate the p-value using a Student's t-distribution: p-value = 0.0054. Graph: s g = 0.866. s b = Reason for decision: p-value < alpha; Conclusion: At the 5% significance level, there is sufficient evidence to conclude that the proportion of family members who shed tears at a reunion is less than 0.60. However, the test is weak because the p-value and alpha are quite close, so other tests should be done p value = 2P(X> 36) = 2P(Z>1:4) = 2(1 0:9192) = 0:1616: Again, using the p value H 0 is not rejected. Example 4 A manufacturer claims that 20% of the public preferred her product. A sample of 100 persons is taken to check her claim. It is found that 8 of these 100 persons preferred her product. a. Find the p-value of the test (use a two-tailed. A study result is stated to be statistically significant if the p-value of the data analysis is less than the prespecified alpha (significance level). In our example, the p-value is 0.02 which is less than the pre-specified alpha of 0.05, so the researcher concludes there is statistical significance for the study

- It is the cutoff probability for p-value to establish statistical significance for a given hypothesis test. For an observed effect to be considered as statistically significant, the p-value of the test should be lower than the pre-decided alpha value. Typically for most statistical tests(but not always), alpha is set as 0.05
- Alpha is the term used to express the level of significance we will accept. For 95% confidence, alpha=0.05. For 99% confidence, alpha=0.01. These two alpha values are the ones most frequently used. If our P-value, the high unlikeliness of the H 0, is less than alpha, we can reject the null hypothesis. Alpha and beta usually cannot both be.
- 11. A hypothesis test gives a p-value of 0.050. If the significance level = 0.05, the results are said to be A. not statistically significant because the p-value is not smaller than . B. statistically significant because the p-value ≤ . C. practically significant because the p-value is the same as
- e the significance of your results. Hypothesis tests are used to test the validity of a claim that is made about a population. This claim that's on trial, in essence, is called the null hypothesis. The alternative hypothesis is the one you would [
- Z-Critical Value for a Two Tailed Test: 2.58: 1.96: 1.645: Notice that two decimal places are given for some values while three are given for others. The applet will accept 1.645 or the rounded 1.65. Note: For all of the examples given in this activity, the conditions np > 5 and nq > 5 are met. This allows us to use the normal distribution to.
- Very often, a p-value less than 0.05 leads us to conclude that there is evidence against the null hypothesis and we say that we reject the same at 5%. A p-value less than 0.01 will under normal circumstances mean that there is substantial evidence against the null hypothesis

- t
**test**: Since**the****p-value**of 0.00000316 is <**alpha**, reject the null hypothesis, and conclude the population mean is**less****than**24 days. Scenario**Two****The**Z and t**test**had same**p-values**: Since**the****p-value**of 0.43 is >**alpha**, fail to reject the null hypothesis, and conclude that the population is equal to 20.9 - It is a hypothesis test in which the critical region is located in both tails of the sampling distribution (for a distribution that actually has two tails). It is not seen all that often because it is basically a tacit admission that the researche..
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