A psychological test inventory called POMS was given to a sample of 25 runners.

Question

A psychological test inventory called POMS was given to a sample of 25 runners. The result showed that the mean was 10.46 with standard deviation of 5.55. A psychologist suspected that, in general, runners have a mean score on POMS that is different from the national norm of 13. (a) At =1%, using the classical approach to test the claim. (b) Using P-value approach to conclude it.

* Please make sure to show all your work to get a partial credit. For instance, on Questions 4, 5, and 6, you must follow such steps as (1) State Ho and Ha, (2) Identify the appropriate distribution and calculate an observed value, and (3) Conduct both Classical and P value approaches for drawing a conclusion. Throughout the exam, you need to draw a picture, shade the area of interest, and obtain either Area or the Cutoff Value from the table. Under the P value approach, you must state how statistically significant Evidence is. You need to state the range for P value and TC to draw a conclusion P value and Classical approaches are completely different approach. (LAST PART VERY IMPORTANT)

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: = 13

Alternative hypothesis: 13

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 1.11

DF = n - 1 = 25 - 1

D.F = 24

t = (x - ) / SE

t = 2.29

tcritical = + 2.797

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the t statistic having 24 degrees of freedom is less than - 2.29 or greater than 2.29.

Thus, the P-value = 0.0311

Interpret results. Since the P-value (0.0311) is less than the significance level (0.01), we have to accept the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that general, runners have a mean score on POMS that is different from the national norm of 13.

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