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.

a)Null hypothesis:      

Alternative hypothesis:      

b) A Type of error I is reject the hypothesis that is equal to 40 when is fact , is different from 40 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 43 hours and that the standard deviation is 4 hours. Based on this information, answer the questions below"

Data given

represent the sample mean

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:      

Alternative hypothesis:      

Part b

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

A Type of error I is reject the hypothesis that 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"