QUESTION 20 The time needed for college students to complete a certain paper and
ID: 3323834 • Letter: Q
Question
QUESTION 20 The time needed for college students to complete a certain paper and pencil maze follows a Normal distribution with a mean of 80 seconds and a standard deviation of 16 seconds. You wish to see if the mean time is changed by meditation, so you have a group of college students meditate for 30 minutes and then complete the maze. It takes them an average of x = 74 seconds to complete the maze. Use this information to test the hypotheses H0: = 80, Ha: 80 at significance level = 0.02. You conclude that a. Ho should be rejected. b. Ho should not be rejected. c. Ha should be accepted. d. this is a borderline case and no decision should be made
Explanation / Answer
Solution:- b) H0, should not be rejected.
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: = 80
Alternative hypothesis: 80
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 0.05. The test method is a one-sample z-test.
Analyze sample data. Using sample data, we compute the standard error (SE),z statistic test statistic (z).
SE = s / sqrt(n)
S.E = 5.657
z = (x - ) / SE
z = - 1.06
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 z statistic less than -1.06 or greater than 1.06.
Thus, the P-value = 0.2892
Interpret results. Since the P-value (0.2892) is greater than the significance level (0.05), we cannot reject the null hypothesis.