Question

A machine in the math lab dispenses coffee. The average cup of coffee is supposed to contain 7 oz. Eight cups of coffee from this machine show the average content to be 7.3 oz. The population standard deviation is 0.5 oz. Do you think the machine has slipped out of adjustment and the average amount of coffee per cup is different from 7 oz? Use a 5% level of significance.

1. stating the null and alternate hypothesis

2. find the p value

3. make your decision to reject or fail to reject the null hypotheses

4. write your conclusion to the problem.

5.  Use the results from above, find a 0.95 confidence interval for the mean number of cups of coffee.

6. Explain in a sentence what the results in #5 mean.

Answer 1

To Test :-

H0 :-

H1 :-  

Test Statistic :-

Z = 1.6971

Test Criteria :-

Reject null hypothesis if

Result :- Fail to reject null hypothesis

Conclusion :- Accept Null Hypothesis

There is no sufficient evidence to support the calim that average amount of coffee per cup is different from 7 oz.

Confidence Interval :-

Lower Limit =

Lower Limit = 6.9535

Upper Limit =

Upper Limit = 7.6465

95% Confidence interval is ( 6.9535 , 7.6465 )

Since   lies in the interval, so we can conclude that the average cup of coffee contain 7 oz.