Question

Some college graduates employed full-time work more than hours per week, and some work fewer than hours per week. We suspect that the mean number of hours worked per week by college graduates, , is different from hours and wish to do a statistical test. We select a random sample of college graduates employed full-time and find that the mean of the sample is hours and that the standard deviation is hours.

Answer 1

Explanation:

What are the null hypothesis (H0) and the alternative hypothesis (H1) that should be used for the test?

A: H0: μ is LESS THAN OR EQUAL TO

H1: μ is GREATER THAN

B: In the context of this test, what is a Type II error?

A Type II error is FAILING TO REJECT the hypothesis that μ is LESS THAN OR EQUAL TO when, in fact, μ is GREATER THAN .

C: Suppose that we decide not to reject the null hypothesis. What sort of error might we be making? TYPE II

Answer 2

a)Null hypothesis:
`\mu =40`

Alternative hypothesis:
`\mu \\eq 40`

b) A Type of error I is reject the hypothesis that
`\mu` is equal to 40 when is fact

Explanation:

Assuming this problem: "Some college graduates employed full-time work more than 40 hours per week, and some work fewer than 40 hours per week. We suspect that the mean number of hours worked per week by college graduates, [tex]\mu" src="

Data given

`\bar X=43` represent the sample mean

`\mu` population mean (variable of interest)

s=4 represent the sample standard deviation

n represent the sample size

Part a: System of hypothesis

We need to conduct a hypothesis in order to determine if actual mean is different from 40 , the system of hypothesis would be:

Null hypothesis:
`\mu =40`

Alternative hypothesis:
`\mu \\eq 40`

Part b

In th context of this tes, what is a Type I error?

A Type of error I is reject the hypothesis that
`\mu` is equal to 40 when is fact [tex]\mu is equal to 40

Part c

Suppose that we decide not to reject the null hypothesis. What sort of error might we be making.

We can commit a Type II Error, since by definition "A type II error is the non-rejection of a false null hypothesis and is known as "false negative" conclusion"