Question

3. It is commonly said that the average college student spends 10 hours per week on the Internet. It is common knowledge that the population standard deviation is 16 hours/week. You believe that the true average time that college students spend on the Internet should not be 10 hours per week, and decide to collect your own sample for a hypothesis test. You randomly sample 250 students from your college and find that on average they spent 12.5 hours a week online.

(a) Write and explain the null and alternative hypotheses.

(b) Write down the test statistic and explain in detail how it is distributed when the null hypothesis is true. Also explain in detail how the test statistic behaves when the null hypothesis is false.

(c) State the probability of Type I Error () you will use in designing your test.

(d) Show in a graph the test rejection region you would use. Be sure to label the distribution of the test statistic when the null hypothesis is true, and indicate where the probability of Type I Error is depicted in your graph.

(e) Show the confidence interval of the mean value and use the evidence to say whether reject or not reject the null hypothesis.

(f) Show the p value of the test statistics and use the evidence to say whether reject or not reject the null hypothesis.

Answer 1

Result:

3. It is commonly said that the average college student spends 10 hours per week on the Internet. It is common knowledge that the population standard deviation is 16 hours/week. You believe that the true average time that college students spend on the Internet should not be 10 hours per week, and decide to collect your own sample for a hypothesis test. You randomly sample 250 students from your college and find that on average they spent 12.5 hours a week online.

(a) Write and explain the null and alternative hypotheses.

To test whether population mean is different from 10 hours.

This is a two tailed test.

(b) Write down the test statistic and explain in detail how it is distributed when the null hypothesis is true. Also explain in detail how the test statistic behaves when the null hypothesis is false.

Since population standard deviation is given, Z test is used.

(c) State the probability of Type I Error () you will use in designing your test.

probability of Type I Error ? = 0.05

(d) Show in a graph the test rejection region you would use. Be sure to label the distribution of the test statistic when the null hypothesis is true, and indicate where the probability of Type I Error is depicted in your graph.

standard normal distribution graph is used.

(e) Show the confidence interval of the mean value and use the evidence to say whether reject or not reject the null hypothesis.

Confidence Interval Estimate for the Mean
Data
Population Standard Deviation	16
Sample Mean	12.5
Sample Size	250
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	1.0119
Z Value	-1.9600
Interval Half Width	1.9833
Confidence Interval
Interval Lower Limit	10.5167
Interval Upper Limit	14.4833

95% confidence interval ( 10.5167, 14.4833). This interval does not contains population mean 10 hrs. we reject the null hypothesis.

(f) Show the p value of the test statistics and use the evidence to say whether reject or not reject the null hypothesis.

Calculated P value = 0.0135 which is < 0.05 level of significance.

Null hypothesis is rejected.

Z Test of Hypothesis for the Mean
Data
Null Hypothesis                       m=	10
Level of Significance	0.05
Population Standard Deviation	16
Sample Size	250
Sample Mean	12.5
Intermediate Calculations
Standard Error of the Mean	1.0119
Z Test Statistic	2.4705
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.0135
Reject the null hypothesis