Q 1

To help make a decision about expansion plans, the president of a music company needs to know how many compact discs teenagers buy annually. Accordingly, he commissions a survey of 250 teenagers. Each is asked to report how many CDs he or she purchased in the previous 12 months. Estimate with 90% confidence the mean annual number of CDs purchased by all teenagers. Assume that the population standard deviation is three CDs. Survey data are in file Xr10-39.

Q2

H _O : µ = 70
H ₁ : µ > 70
σ = 20, n = 100, xbar = 80, α = .01
a) calculate the value of the test statistic
b) set up the rejection region.
c) determine the p-value
d) interpret the results

Q3

1. given the following hypotheses, determine the p-value when xbar = 21, n = 25, and σ = 5.
   H _o : µ = 20
   H ₁ : µ ≠ 20
2. repeat part (a) with xbar = 22.
   c) repeat part (a) with xbar = 23.
   d) describe what happens to the value of the test statistic and its p-value when the value of xbar increases.

Answer

Q4

1. Calculate the probability of a type ii error for the following hypotheses when µ = 37:

h _o : µ = 40
h ₁ : µ < 40
the significance level is 5%, the population standard deviation is 5, and the sample size is 25.
b) repeat part (a) with α = 15%.
c) describe the effect on β of decreasing α.

Q5

Calculate the following:

Determine the sample size necessary to estimate a population mean to within 1 with a 90% confidence given that the population standard deviation is 10.
b) Suppose that the sample was calculated at 150. Estimate the population mean with 90% confidence.

Q6

Bursaries are loans made to students who need the money to support themselves while attending universities and colleges. The loans are made by banks that are guaranteed repayment by the government. A government auditor wanted to know the status of the loans made to students at one university. He randomly sampled 188 of the 2,684 loans that are outstanding. The total amounts owing were recorded. Estimate with 90% confidence the total outstanding amount of the loans made to students at the university. data are in file Xr12-103.

Q7

1. From the information given here, determine the 95% confidence interval estimate of the population mean.

   Xbar = 100

   σ = 20

   n = 25

2. Repeat part (a) with xbar = 200.
   c) Repeat part (a) with xbar = 500
   d) Describe what happens to the width of the confidence interval estimate when the sample mean increases.

Q8

Surveys have been widely used by politicians around the world as a way of monitoring the opinions of the electorate. Six months ago, a survey was undertaken to determine the degree of support for a national party leader. Of a sample of 1,100, 56% indicated that they would vote for this politician. This month, another survey of 800 voters revealed that 46% now support the leader.

1. At the 5% significance level, can we infer that the national leader's popularity has decreased?
   b) At the 5% significance level, can we infer that the national leader's popularity has decreased by more than 5%?
   c) Estimate with 95% confidence the decrease in percentage support between now and 6 months ago.

Q9

Determine the sample size necessary to estimate a population proportion to within .03 with 90% confidence assuming you have no knowledge of the approximate value of the sample proportion.

Q10

The golf professional at a private course claims that members who have taken lessons from him lowered their handicaps by more than 5 strokes. The club manager decides to test the claim by randomly sampling 25 members who have had lessons and asks each to report their reduction in handicap. These data are stored in file Xr11-45 on the student CD. A negative number represents an increase in handicap. Assuming that the reduction in handicap is approximately normally distributed with a standard deviation of 2 strokes, test the golf professional’s claim using a 10% significance level.

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