Question

1) A demographer wants to measure life expectancy in countries 1 and 2. Let μ1 and μ2 denote the mean life expectancy in countries 1 and 2, respectively. Specify the hypothesis to determine if life expectancy in country 1 is more than 10 years lower than in country 2.

A) H0:μ1– μ2≤10, HA:μ1– μ2>10

B) H0:μ1– μ2≥10, HA: μ1– μ2<10

C)H0:μ1– μ2≤–10, HA:μ1– μ2>−10

D)H0:μ1– μ2≥–10, HA:μ1– μ2<−10

2) A restaurant chain has two locations in a medium-sized town and, believing that it has oversaturated the market for its food, is considering closing one of the restaurants. The manager of the restaurant with a downtown location claims that his restaurant generates more revenue than the sister restaurant by the freeway. The CEO of this company, wishing to test this claim, randomly selects 36 monthly revenue totals for each restaurant. The revenue data from the downtown restaurant have a mean of $360,000 and a standard deviation of $50,000, while the data from the restaurant by the freeway have a mean of $340,000 and a standard deviation of $40,000. Assume there is no reason to believe the population standard deviations are equal, and let μ1 and μ2 denote the mean monthly revenue of the downtown restaurant and the restaurant by the freeway, respectively. Which of the following hypotheses should be used to test the manager's claim?

A) H0:μ1– μ2≤0, HA:μ1– μ2>0

B) H0:μ1– μ2 ≥0 , HA:μ1– μ2<0

C) H0:μ1– μ2=0, HA:μ1– μ2≠0

D) H0:μ1– μ2>0, HA:μ1– μ2≤0

3) what the formula for the sample variance s2 when used as an estimate of σ2 for a random sample of n observations from a population?

4)What is the formula for the sample variance s2 when used as an estimate of σ2 for a random sample of n observations from a population? 46)  A financial analyst examines the performance of two mutual funds and claims that the variances of the annual returns for the bond funds differ. To support his claim, he collects dataon the annual returns (in percent) for the years 2001 through 2010. The analyst assumes that the annual returns for the two emerging market bond funds are normally distributed. Use the following summary statistics.

s1^2=500	s2^2=100
n1=10	n2=10

For the competing hypotheses Η0: σ1^2/ σ2^2=1, ΗA:σ1^2/ σ2^2≠ 1, which of the following is the correct approximation of the p-value?

A) Less than 0.01

B) Between 0.01 and 0.025

C) Between 0.02 and 0.05

D) Between 0.05 and 0.1

5) ) The following table shows the distribution of employees in an organization. Martha Foreman,an analyst, wants to see if race has a bearing on the position a person holds with this company

race	coordinator	analyst	manager	director
white	32	20	25	9
black	35	10	25	5
hispanic	32	15	13	2
asian	10	11	10	0

Using the p-value approach and α= 0.05, the decision and conclusion are ________.

A) reject the null hypothesis; conclude race and seniority are dependent

B) reject the null hypothesis; conclude race and seniority are independent

C) do not reject the null hypothesis; cannot conclude race and seniority are dependent

D) do not reject the null hypothesis; conclude race and seniority are independent

Answer 1

Ans 1 ) the null and alternative hypothesis is given by option d

D)H0:μ1– μ2≥–10

HA:μ1– μ2<−10 (one tailed )

Ans 2 ) the null and alternative hypothesis is given by option A

A) H0:μ1– μ2≤0, HA:μ1– μ2>0

ANs 3 ) the formula for the sample variance s2 when used as an estimate of σ2 for a random sample of n observations from a population

Ans 4 )using minitab>stat>basic stat>2 variance

we have

Test and CI for Two Variances

Method

Null hypothesis σ(First) / σ(Second) = 1
Alternative hypothesis σ(First) / σ(Second) ≠ 1
Significance level α = 0.05

F method was used. This method is accurate for normal data only.

Statistics

95% CI for
Sample N StDev Variance StDevs
First 10 22.361 500.000 (15.380, 40.822)
Second 10 10.000 100.000 ( 6.878, 18.256)

Ratio of standard deviations = 2.236
Ratio of variances = 5.000

95% Confidence Intervals

CI for
CI for StDev Variance
Method Ratio Ratio
F (1.114, 4.487) (1.242, 20.130)

Tests

Test
Method DF1 DF2 Statistic P-Value
F 9 9 5.00 0.025

Η0: σ1^2/ σ2^2=1, ΗA:σ1^2/ σ2^2≠ 1
option c is true

C) Between 0.02 and 0.05

Ans 5 ) the p value of chi square is 0

B) reject the null hypothesis; conclude race and seniority are independent