Hi, I just wrote a North American knowlege quiz for statistics and probabillity.

These were the questions. Can someone solve any of these and show your work? I just need to check if i did it correctly... nervous....

Long Answer Questions

3. In an investigation of pregnancy-induced hypertension, one group of women with this

disorder was treated with low-dose aspirin, and a second group was given a placebo. A

sample consisting of 23 women who received aspirin has mean arterial blood pressure

111 mm Hg and standard deviation 8 mm Hg; a sample of 24 women who were given

the placebo has mean blood pressure 109 mm Hg and standard deviation 8 mm Hg.

a. [5] At the 0.01 level of signicance, test the null hypothesis that the two populations

of women have the same mean arterial blood pressure.

b. [4] Construct a 99% condence interval for the true dierence in population means.

Does this interval contain the value 0?

4. [8] Online ads targeting children were said to have decreased at least 56% between

May and August 2000. A sample of 100 ads selected during this period showed a 45%

decrease in online ads targeting children. State the null and alternative hypotheses

and carry out the test at the 1% level of signicance.

5. A fast food franchiser is considering building a restaurant at a certain location. Ac-

cording to a nancial analysis, a site is acceptable only if the number of pedestrians

passing the location averages more than 100 per hour. A random sample of 50 hours

produced x = 110 and s = 12 pedestrians per hour.

a. [5] Do these data provide sucient evidence to establish that the site is acceptable?

Use = 0:05.

b. [3] What are the consequences of Type I and Type II errors? Which error is more

expensive to make?

c. [2] Considering your answer in part (b), should you select to be large or small?

Explain.

d. [3] What assumptions about the number of pedestrians passing the location in an

hour are necessary for your hypothesis test to be valid?

6. [10] A company is interested in oering its employees one of two employee benet

packages. A random sample of the company's employees is collected, and each person

in the sample is asked to rate each of the two packages on an overall preference scale

of 0 to 100. Results were

Program A: 45, 67, 63, 59, 77, 69, 45, 39, 52, 58, 70

Program B: 56, 70, 60, 45, 85, 79, 50, 46, 50, 60, 82

Do you believe that the employees of this company prefer, on the average, one package

over the other? Explain.

7. [10] Data from the Bureau of Labor Statistics indicate that in one recent year the

unemployment rate in Cleveland was 7.5% and unemployment rate in Chicago was

7.2%. Suppose that both gures are based on random samples of 1,000 people in each

city. Test the null hypothesis that the unemployment rates in both cities are equal

versus the alternative hypothesis that they are not equal. What is the p-value? State

your conclusion.

2

8. A chemical manufacturer claims that the purity of his product never varies by more

than 2%. Five batches were tested and given purity reading of 98.2, 97.1, 98.9, 97.7,

and 97.9%.

a. [4] Do the data provide sucient evidence to contradict the manufacturer's claim?

(To be generous, let a range of 2% equal 4.)

b. [4] Find a 90% condence interval for 2.

c. [2] Under which conditions, the condence interval and test hypothesis in part (a)

and (b) are valid?

9. The following data were obtained in an experiment relating the dependent variable, y

(texture of strawberries) , with x (coded storage temperature).

x -2 -2 0 2 2

y 4.0 3.5 2.0 0.5 0.0

a. [4] Calculate the correlation coecient between x and y.

b. [6] What is the regression line for predicting texture of strawberries based on coded

storage temperature.