Question

A sample of 34 observations is selected from a normal population. The sample mean is 15, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.10 significance level. H0: μ ≤ 14 H1: μ > 14

Required:
a. Compute the value of the test statistic.
b. What is the p-value?

Answer 1

1.944 ;

0.026

Explanation:

Given :

Sample size, n = 34

Sample mean, xbar = 15

Population standard deviation, σ = 3

The hypothesis :

H0: μ ≤ 14

H1: μ > 14

The test statistic :

Test statistic = (xbar - μ) ÷ (σ/√(n))

Test statistic = (15 - 14) ÷ (3/√(34))

Test statistic = 1 / 0.5144957

Test statistic, Z = 1.944

The Pvalue :

Using the Pvalue from test statistic value :

Pvalue(1.944) = 0.026

Pvalue < α ; Reject H0