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An internet service provider (ISP) provides internet connections

Question # 00013866
Subject: Statistics
Due on: 04/29/2014
Posted On: 04/29/2014 03:23 AM

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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.
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 285, and the sample standard deviation of the number of emails in the the month is 135. For low-speed-connection customers, the sample mean number of emails in the month is 279, and the sample standard deviation of the number of emails in the month is 142.
(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)?


At a particular university in an urban area, official policy mandates that university-owned student housing shall rent for no more than 80% of the market rate for comparable housing. Rent for all two-bedroom university-owned student apartments is $630/month. All the university-owned two-bedroom student apartments have one bathroom, no view, and are comparable in construction, size, age, amenities, etc. To determine whether the rent satisfies the rules, an administrator proposes to compile as complete a list as he can of two-bedroom apartments for rent in the area, using sources including newspaper ads, commercial rental listing services, and bulletin boards. Then, he will take a simple random sample of 150 of the apartments in the list, and visit each one to determine whether it is comparable to the university-owned apartments in size, number of bathrooms, state of repair, amenities (such as laundry facilities, bathtub/shower), etc. He will compute the sample mean rent of those apartments he finds to be comparable to the university-owned apartments. Let r denote the mean rent of all comparable two-bedroom apartments in the area, and let R denote the sample mean rent of the comparable two-bedroom apartments the administrator finds. The administrator will approach the problem of determining whether the university is complying with the mandate as an hypothesis test.


The most appropriate alternative hypothesis is (Q13): r or R (Q14): <, =, or >? than (Q15) $____?


Suppose that the administrator finds that 30 of the apartments are comparable to two-bedroom university-owned student apartments. Assume that
these 30 apartments can be treated as a random sample of size 30 with replacement from the population of comparable two-bedroom apartments for rent in the area, and
the distribution of rents for comparable apartments in the area is approximately normal.
Suppose that the sample mean of the rents is $768 and the sample standard deviation of the rents is $105.

(Q16): The estimated standard error of the sample mean is $___?
(Q17): The number of degrees of freedom for Student's t-curve to approximate the probability histogram of the T statistic is___?
(Q18): The observed value of the T statistic is ___?
(Q19): The P-value of the null hypothesis is ___?


A (two-sided) 90% confidence interval for the mean rent of comparable two-bedroom apartments in the area is from $ (Q20) (low) to $ (Q21) (high).

Tags internet connections provides provider service sample apartments customers number comparable hypothesis standard emails rent month connections mean twobedroom sent deviation area null universityowned received test previous denote random highspeed administrator lowspeed student suppose finds appropriate

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Tutorial Preview …Sh xx the xxxxxx standard deviation xx the number xx emails xxxx xxx received xx the previous xxxxx by customers xxxx high-speed xxxxxxxxxxxx xxx let xx be the xxxxxx standard deviation xx the xxxxxx xx emails xxxx and received xx the previous xxxxx by xxxxxxxxx xxxx low-speed xxxxxxxxxxx (Q1) Which xx these hypotheses xx the xxxx xxxxxxxxxxx null xxxxxxxxxx for this xxxxxxxxxx h > xxx H xxxx xxx h xxxx lD: H x LE: H xxxx LF: x x l(Q2) xxxxx of these xxxxxxxxxx is the xxxx appropriate xxxxxxxxxxx xxxxxxxxxx for xxxx problem?A: h x lB: H xxxx LC: x x LD: x < LE: x < lF: x > xxxxx xxxxxxx that xxx population distributions xx the number xx emails xxxx xx the xx high-speed-connection customers xxx by low-speed-connection xxxxxxxxx both xxx xxxxxx normal xxxxx of the xxxxxxxxx have probability xxxxxxxxxx that xxx xx approximated xxxx by a xxxxxx curve, after xxxxxxxxxxxx to xxxxxxxx xxxxxx (select xxx that apply)A: xxx H-LC: HD: xxx h x xxx h(Q4):Suppose xx construct a x…
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Preview: will xxxx a xxxxxx random sample xx 150 of xxx apartments xx xxx list, xxx visit each xxx to determine xxxxxxx it xx xxxxxxxxxx to xxx university-owned apartments xx size, number xx bathrooms, xxxxx xx repair, xxxxxxxxx (such as xxxxxxx facilities, bathtub/shower), xxx He xxxx xxxxxxx the xxxxxx mean rent xx those apartments xx finds xx xx comparable xx the university-owned xxxxxxxxxx Let r xxxxxx the xxxx xxxx of xxx comparable two-bedroom xxxxxxxxxx in the xxxxx and xxx x denote xxx sample mean xxxx of the xxxxxxxxxx two-bedroom xxxxxxxxxx xxx administrator xxxxx The administrator xxxx approach the xxxxxxx of xxxxxxxxxxx xxxxxxx the xxxxxxxxxx is complying xxxx the mandate xx an xxxxxxxxxx xxxx The xxxx appropriate alternative xxxxxxxxxx is (Q13): x or x xxxxxx <, xx or >? xxxx (Q15) $787 xxxxxxxxxx that xxx xxxxxxxxxxxxx finds xxxx 30 of xxx apartments are xxxxxxxxxx to xxxxxxxxxxx xxxxxxxxxxxxxxxx student xxxxxxxxxx Assume thatthese xx apartments can xx treated xx x random xxxxxx of size xx with replacement xxxx the xxxxxxxxxx xx comparable xxxxxxxxxxx apartments for xxxx in the xxxxx andthe.....
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