Question

15A somewhat outdated study indicates that the mean number of hours worked per week by software developers is 44. We have good reason to suspect that the mean number of hours worked per week by software developers, μ, is now greater than 44 and wish to do a statistical test. We select a random sample of software developers and find that the mean of the sample is 48 hours and that the standard deviation is 4 hours.Based on this information, complete the parts below.(a)What are the null hypothesis H0 and the alternative hypothesis H1 that should be used for the test?H0:H1:(b)Suppose that we decide to reject the null hypothesis. What sort of error might we be making?type 1 or type 2?(c) Suppose the true mean number of hours worked by software engineers is 50 hours. Fill in the blanks to describe a Type II error.A Type II error would be ______ the hypothesis that μ is ______, ______ when, in fact, μ is ______.

Answer 1

Part A:

The null hypothesis is the commonly accepted fact. It is the opposite of the alternative hypothesis for which the researchers have a good reason to suspect.

The null and alternative hypothesis are the following:

H₀: μ = 44 (Since it is established that the mean number of hours per week is 44)

H₁: μ > 44 (Since the researchers suspect that it is greater than 44)

Part B:

This table simplifies the type of errors that could be committed when rejecting or accepting the null hypothesis.

Should we reject the null hypothesis, but it turns out to be true. Then the error that we have committed is Type I.

Part C:

A Type II error happens when we fail to reject the null hypothesis when in fact the alternative hypothesis is true.

Suppose that the true mean number of hours worked by software engineers is 50 hours, then a type II error would be failing to reject the hypothesis that μ is equal to 44, when in fact μ is greater than 44.