Question

In order to conduct a hypothesis test of the population mean, a random sample of 28 observations is drawn from a normally distributed population. The resulting mean and the standard deviation are calculated as 17.9 and 1.5, respectively. Use Table 2.

Use the p-value approach to conduct the following tests at α = 0.10.

H0: μ ≤ 17.5 against HA: μ > 17.5

a-1.	Calculate the value of the test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Test statistic

a-2.	Approximate the p-value.
	0.010 < p-value < 0.020 0.020 < p-value < 0.050 0.050 < p-value < 0.100

a-3.	What is the conclusion?
	Do not reject H0 since the p-value is greater than α. Reject H0 since the p-value is greater than α. Reject H0 since the p-value is smaller than α. Do not reject H0 since the p-value is smaller than α.

H0: μ = 17.5 against HA: μ ≠ 17.5

b-1.	Calculate the value of the test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Test statistic

b-2.	Approximate the p-value.
	0.010 < p-value < 0.020 0.100 < p-value < 0.200 0.050 < p-value < 0.100

b-3.	What is the conclusion?
	Reject H0 since the p-value is smaller than α. Do not reject H0 since the p-value is smaller than α. Do not reject H0 since the p-value is greater than α. Reject H0 since the p-value is greater than α.

Answer 1

The statistical software output for this problem is:

One sample T summary hypothesis test: H Mean of population Ho 17.5 HA: H17.5 Hypothesis test results: Mean Sample Mean Std. Err. P-value DF T-Stat 0.0848 17.9 0.28347335 27 1.4110674|

Hence,

a - 1) Test statistic = 1.41

a - 2) 0.050 < p-value < 0.100

a - 3) Reject H₀ since the p-value is smaller than α.

b - 1) Test statistic = 1.41

b - 2) 0.100 < p-value < 0.200

b - 3) Do not reject H₀ since the p-value is greater than α.