Question

1.Market researchers were comparing the true proportion of Lifetime Movie Club subscribers who prefer the original Stalked by My Doctor movie vs the follow-up sequel, Stalked by My Doctor: The Return. They obtained the 80% confidence interval below.

0.18 < p1 - p2 < 0.26

Which is the best choice for the margin of error?

a.  0.02

b. 0.08

c. 0.22

d. 0.20

e.0.04

2.Country music sensation Whiskey Horse Boots historically sells out 92.7% of their arena shows. Assuming the appropriate probability modeling requirements are met, compute the probability they sell out exactly two of the remaining four shows.

A.0.027

B. 0.309

  C.0.185

  D.0.233

E. 0.146

3.The time it takes to be seated for a party of five at Hookah Joe's on a Friday night is normally distributed with a mean of 12.3 minutes and a standard deviation of 3.2 minutes. What is the probability it takes at least 15 minutes to be seated?

A.0.8438

B. 0.2005

C. 0.7005

D. 0.2995

4.Rumor has it that the mean salary of dog catchers in Idaho is 49.8 years. If a hypothesis test is performed, and thep-value is not smaller than alpha, how should you interpret the decision?

A.There is not sufficient evidence to reject the claim μ = 49.8.

  B.There is sufficient evidence to support the claim μ = 49.8.

C. There is not sufficient evidence to support the claim μ = 49.8.

D. There is sufficient evidence to reject the claim μ = 49.8.

5.In the 2012 study Age at Onset Versus Family History and Clinical Outcomes in 1,665 International Bipolar-I Disorder Patients, Harvard researchers indicated that "age of onset" was approximately normal with a mean of 23 years and a standard deviation of 11 years. For the 1,665 patients in the study, how many would you approximate were at least 18 years of age for their onset of bipolar-I disorder? Select the single best choice.

a.289

b. 1207

c. 1122

d.  543

 

Answer 1

1. Lower limit of CI: u - MOE = 0.18
Upper limit: u + MOE = 0.26

MOE = (0.26 - 0.18)/2 = 0.04
Correct option: E) 0.04

2. P(Sell out) = p = 0.927
n = 4

This is a binomial distribution.
P(2) = 4C2 * (0.927)^2 * (0.073)^2 = 0.027
Correct option: A)

3. u = 12.3
s = 3.2

We need to find: P(X > 15)
= P(z > (15 - 12.3)/3.2)
= P(z > 0.84)
= 1 - P(z < 0.84)

From the z-table,

= 1 - 0.7995
= 0.2005
Correct option: B)

4. As the p-value is not smaller than alpha, we fail to reject Ho. We will say that there is not sufficient evidence to reject the claim u = 49.8 (Ho)
Correct option: A)

5. u = 23, s = 11

P(X > 18) = P(z > (18-23)/11)
= P(z > -5/11)
= P(z > -0.45)
= 1 - P(z < -0.45)
= 1 - 0.3264
= 0.6736

The number of people who were atleast 18 years old = 0.6736*1665 = 1122
Correct option: C) 1122