Question

The manager of a pizza restaurant claims his employees make an average of $8.00 per hour with a standard deviation of $0.75. Jack does not believe the manager's claim, so he takes a sample of 40 employees and finds their average salary to be $7.80. Jack tests the manager's claim at

1. Jack should reject the null hypothesis if the test statistic is less than or equal to the value of ?

or greater than or equal to the value of ?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 8
Alternative Hypothesis, Ha: μ < 8

Rejection Region
This is left tailed test, for α = 0.05
Critical value of z is -1.645.
Hence reject H0 if z < -1.645

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (7.8 - 8)/(0.75/sqrt(40))
z = -1.687

P-value Approach
P-value = 0.0458
As P-value < 0.05, reject the null hypothesis.

1. Jack should reject the null hypothesis if the test statistic is less than or equal to the value of -1.645