Problem 1

An internet service provider (ISP) provides internet connections to 100,000 customers. 10,000 of the customers have high-speed connections and 90,000 of the customers have low-speed connections. The ISP wants to know whether, on the average, customers who have high-speed connections use email more frequently than customers who have low-speed connections. To find out, the ISP takes a simple random sample of 150 high-speed-connection customers and an independent random sample of 300 low-speed-connection customers. For each customer in the sample, they find the number of emailmessages sent and received in the previous month. Then they compute the sample mean and sample standard deviation of each of the two sets of numbers.

Let h denote the average number of emails sent and received in the previous month among all customers with high-speed connections, and let l denote the average number of emails sent and received in the previous month among all customers with low-speed connections. Let H and L be the corresponding sample means. Let Sh be the sample standard deviation of the number of emails sent and received in the previous month by customers with high-speed connections, and let Sl be the sample standard deviation of the number of emails sent and received in the previous month by customers with low-speed connections.

Questions:

Which of these hypotheses is the most appropriate null hypothesis for this problem? (Q1)

A) H=L

B) H>L

C) h=l

D) h

E) h>l

F) H

Which of these hypotheses is the most appropriate alternative hypothesis for this problem? (Q2)

A) H=L

B) H>L

C) h=l

D) h

E) h>l

F) H

Suppose that the population distributions of the number of emails sent in the by high-speed-connection customers and by low-speed-connection customers both are nearly normal. Which of the following have probability histograms that can be approximated well by a normal curve, after transforming to standard units? (select all that apply) (Q3)

A) H-L

B) L

C) h

D) h-l

E) l

F) H

Suppose we construct a Z statistic by transforming H - L to standard units (approximately). Under the alternative hypothesis, the expected value of Z would be (Q4)

A) Negative

B) Zero

C) Positive

, so we should (Q5)

A) use a two-tail test

B) use a right tail test

C) consult a statistician

D) use a left tail test

To test the null hypothesis at significance level 10%, we should reject the null hypothesis if the z score is greater than: __ ? (Q6)

For high-speed-connection customers, the sample mean number of emails in the month is 284, and the sample standard deviation of the number of emails in the the month is 89. For low-speed-connection customers, the sample mean number of emails in the month is 261, and the sample standard deviation of the number of emails in the month is 100.

The estimated standard error of H - L is:__ ? (Q7)

The z-score is:__ ? (Q8)

The P-value of the null hypothesis is:__ ? (Q9)