27. H0: mean = 7 H1: mean =- 7 A test is performed with a sample of size 36. The
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Question
27. H0: mean = 7 H1: mean =- 7 A test is performed with a sample of size 36. The sample mean was 2.76 and the population standard deviation is 18. Assume that the population is approximately normal. Use the TI-84 PLUS calculator to compute the P-value. 28. H0: mean = 16 H1: mean < 16 A test is performed with a sample of size 100. The sample mean was 6.65 and the population standard deviation is 60. Assume that the population is approximately normal. Use the TI-84 PLUS calculator to compute the P-value.27. H0: mean = 7 H1: mean =- 7 A test is performed with a sample of size 36. The sample mean was 2.76 and the population standard deviation is 18. Assume that the population is approximately normal. Use the TI-84 PLUS calculator to compute the P-value. 28. H0: mean = 16 H1: mean < 16 A test is performed with a sample of size 100. The sample mean was 6.65 and the population standard deviation is 60. Assume that the population is approximately normal. Use the TI-84 PLUS calculator to compute the P-value.
27. H0: mean = 7 H1: mean =- 7 A test is performed with a sample of size 36. The sample mean was 2.76 and the population standard deviation is 18. Assume that the population is approximately normal. Use the TI-84 PLUS calculator to compute the P-value. 28. H0: mean = 16 H1: mean < 16 A test is performed with a sample of size 100. The sample mean was 6.65 and the population standard deviation is 60. Assume that the population is approximately normal. Use the TI-84 PLUS calculator to compute the P-value.
Explanation / Answer
Solution:-
28)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: u > 16
Alternative hypothesis: u < 16
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.01. 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 = 6.00
z = (x - u) / SE
z = - 1.56
where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a z statistic test statistic of - 1.56.
Thus the P-value in this analysis is 0.059.
Interpret results. Since the P-value (0.059) is greater than the significance level (0.01), we cannot reject the null hypothesis.
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