Consider the following hypotheses: H0: 76.7 HA: > 76.7 A sample of 41 observatio

Question

Consider the following hypotheses: H0: 76.7 HA: > 76.7 A sample of 41 observations yields a sample mean of 78.0. Assume that the sample is drawn from a normal population with a known population standard deviation of 4.4. Use Table 1. a. Calculate the p-value. (Round p-value to 4 decimal places.) 0.05 Picture p-value < 0.10 p-value Picture 0.10 p-value < 0.01 0.01 Picture p-value < 0.025 0.025 Picture p-value < 0.05 b. What is the conclusion if = 0.10? Do not reject H0 since the p-value is smaller than . Do not reject H0 since the p-value is greater than . Reject H0 since the p-value is smaller than . Reject H0 since the p-value is greater than . c. Calculate the p-value if the above sample mean was based on a sample of 148 observations. (Round p-value to 4 decimal places.) p-value < 0.01 0.01 Picture p-value < 0.025 0.025 Picture p-value < 0.05 0.05 Picture p-value < 0.10 p-value Picture 0.10 d. What is the conclusion if = 0.10? Reject H0 since the p-value is smaller than . Reject H0 since the p-value is greater than . Do not reject H0 since the p-value is smaller than . Do not reject H0 since the p-value is greater than .

Explanation / Answer

The statistical software outputs for n = 41 and n = 148 are:

One sample Z summary hypothesis test:
: Mean of population
H0 : = 76.7
HA : > 76.7
Standard deviation = 4.4

Hypothesis test results:

Hypothesis test results:

Hence,

a) 0.025 < p - value < 0.05

b) Reject H0 since the p-value is smaller than .

c) p-value < 0.01

d) Reject H0 since the p-value is smaller than .

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