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 300 high-speed-connection customers and an independent random sample of 350 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. 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. Q1) Which of these hypotheses is the most appropriate null hypothesis for this problem?
A: h > l
B: H > L
C: h < l
D: H = L
E: H < L
F: h = l
Q2) Which of these hypotheses is the most appropriate alternative hypothesis for this problem?
A: h = l
B: H > L
C: H = L
D: H < L
E: h < l
F: h > l
(Q3) 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)
A: L
B: H-L
C: H
D: I
E: h - l
F: h
(Q4): 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:
A: Negative
B: zero
C: Positive
(Q5): So we should:
A: consult a statistician
B: use a left-tail test
C: use a right-tail test
D: use a two-tail test
(Q6) To test the null hypothesis at significance level 1%, we should reject the null hypothesis if:
A: the z-score
B: the absolute value of the z-score
(Q7)is
A: less than
B: greater than
(Q8)? (continues from q6 and q7)
For high-speed-connection customers, the sample mean number of emails in the month is 283, and the sample standard deviation of the number of emails in the the month is 102. For low-speed-connection customers, the sample mean number of emails in the month is 255, and the sample standard deviation of the number of emails in the month is 137.
(Q9) The estimated standard error of H - L is___?
(Q10) The z-score is ___?
(Q11): The P-value of the null hypothesis is___?
(Q12): The ISP should reject the null hypothesis. (true/false)?