Problem1.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 200 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 email messages 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.

Lethdenote the average number of emails sent and received in the previous month among all customers with high-speed connections, and letldenote the average number of emails sent and received in the previous month among all customers with low-speed connections. LetHandLbe the corresponding sample means. LetS_hbe the sample standard deviation of the number of emails sent and received in the previous month by customers with high-speed connections, and letS_lbe the sample standard deviation of the number of emails sent and received in the previous month by customers with low-speed connections.

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 = l

E: H = L

F: h < l

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 > L

E: h > l

F: h < l

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: l

B: H - L

C: h - l

D: L

E: h

F: H

Suppose we construct aZstatistic by transformingH-Lto standard units (approximately).Under the alternative hypothesis, the expected value ofZwould be(Q4) ?

A: negative

B: zero

C: positive

, so we should(Q5) ?

A: consult a statistician

B: use a right-tail test

C: use a left-tail test

D: use a two-tail test

To test the null hypothesis at significance level 1%, we should reject the null hypothesis if(Q6) ?

A: the z-score

B: the absolute value of the z-score

(Q7) ?

A: is less than

B: is greater than

(Q8)

Note: I do not need help with questions 1-8, just the ones that follow.

For high-speed-connection customers, the sample mean number of emails in the month is 428, and the sample standard deviation of the number of emails in the the month is 64. For low-speed-connection customers, the sample mean number of emails in the month is 409, and the sample standard deviation of the number of emails in the month is 147.

The estimated standard error ofH-Lis(Q9)(asked the TA about this and he says that this means the estimated standard error of the difference between H and L.)

I know the formula for the standard error is the following:

standard deviation/ square root of sample population

And that H= 428 and L=409

And that the SD of h= 64 and the SD of l=147

I am having a hard time combining everything to find the standard error for H-L.

Thez-score is(Q10)

I know that the z score formual is : x-(sample mean )/standard deviation

I am having a. hard time idenitfying these values. What would x be here? For the sample mean and the standard deviation how do we combine both for H and L?

TheP-value of the null hypothesis is(Q11)

I know how to find the P Value, once I have the z score.

The ISP should reject the null hypothesis.(Q12) ?

A: false

B: true