# Independent random samples were taken from normal distributions

1. Independent random samples were taken from normal distributions of the yearly production of ships built by the International Ship Building Company under (a) a fixed-position layout (sample size = 7) and (b) a project layout (sample size = 8). The company wants to know if the variances in the yearly production of ships for the 2 layouts are equal. The sample variances (s2) are: fixed-position layout = 9, project layout = 4. Using a = .10, what formula would you use?

(Points : 5)

χ² = ∑ (fij – eij)2 ÷ eij

F = s12 ÷ s22

x̄ = ∑ x ÷ n

s2 = ∑(x – x̄)2 ÷ (n – 1)

2. Suppose that a random sample of 25 retail merchants from all of the 5,000 merchants in a large city yielded a mean advertising expense (x̄) for the past year of $1,250. If the annual advertising expenditures are known to be normally distributed and the standard deviation of the population (σ) is $750, what formula would you use to determine the 95% confidence interval for the true mean advertising expense?

(Points : 5)

F = s12 ÷ s22

x̄ – t(s ÷ √n) < µ < x̄ + t(s ÷ √n)

z = (x – µ) ÷ σ

x̄ – z(σ ÷ √n) < µ < x̄ + z(σ ÷ √n)

3. The average gasoline price (µ) of one of the major oil companies in Europe has been $1.25 per liter with a population standard deviation of the population (σ) of $0.14. Recently, the company has undertaken several efficiency measures in order to reduce prices. Management is interested in determining whether their efficiency measures have actually reduced prices. A random sample of 49 of their gas stations is selected and the average price (x̄) is determined to be $1.20 per liter. What formula would you use to determine whether the new efficiency measures were effective? (a = 0.05)

(Points : 5)

F = s12 ÷ s22

t = (x̄ – μx-bar) ÷ s/√n

z = (x̄ – μx-bar) ÷ σ/√n

ŷ = b0 + b1x

4. On the most recent tax cut proposal, a random sample of democrats and republicans in the Congress cast their votes as shown below. Are the opinions on the tax cut proposal independent of party affiliation? Use a = 0.01.

Favor Oppose Abstain

Democrat 85 78 37

Republican 118 61 25

5. An automobile manufacturer has a new model that they claim gets 27 miles per gallon. A consumer testing agency selects 50 of these cars and finds that the sample mean (x̄) is 25 miles per gallon and s2 = 9 miles per gallon. Is the manufacturer’s claim accurate? (a = 0.05)

6. Is there a significant difference in automobile insurance rates in different cities of comparable size in the U.S.? To answer this question a survey was taken in 3 cities. A sample of 6 auto insurance premiums was taken for married, male drivers, over 35 years-of-age, with no accidents in the last 5 years. The table below contains semi-annual premiums for equal policy coverage. Test the appropriate hypothesis at the 0.05 level of significance.

Baton Rouge Fresno Tulsa

96 124 82

128 149 124

83 166 132

61 147 135

101 149 109

78 130 121