Question

The CEO of the company claims that the mean work day of the company’s mechanical engineers is less than 8.5 hours. A random sample of 25 of the company’s mechanical engineers has a mean work of 8.2 hours. Assume the population standard deviation is 0.5 hour and the population is normally distributed. At ​​α​​​​ = 0.01, test the CEO’s claim.

• State Ho and Ha and identify the claim.
• State the tail of the hypothesis test.
• State the level of significance.
• State the critical value and explain why you chose a z or a t-test.
• Complete the hypothesis test.
• State your conclusion.
• Discuss the possibility of a Type I or Type II error.

Answer 1

Here, we have to use one sample z test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: H0: the mean work day of the company’s mechanical engineers is 8.5 hours.

Alternative hypothesis: Ha: the mean work day of the company’s mechanical engineers is less than 8.5 hours.

H0: µ = 8.5 versus Ha: µ < 8.5

This is a two tailed test.

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 8.5

Xbar = 8.2

σ = 0.5

n = 25

α = 0.01

Critical value = -2.3263

(by using z-table or excel)

Z = (8.2 – 8.5)/[0.5/sqrt(25)]

Z = -3.0000

P-value = 0.0013

(by using Z-table)

P-value < α = 0.01

So, we reject the null hypothesis

There is sufficient evidence to conclude that the mean work day of the company’s mechanical engineers is less than 8.5 hours.