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.

Answer 1

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.