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# Two -Sample Tests of Hypothesis

Exercise 27:
A recent study focused on the number of times men and women who live alone buy take-out in a month. The information is summarized below

Statistic Men Women
Sample Mean 24.51 22.69
Population Standard Deviation 4.48 3.86
Sample Size 35 40

At the .01 significance level, is there a difference in the mean number of times men and women order take out dinners in a month? What is the p-value?

Exercise 46
Grand Strand Family Medical center is specifically set up to treat minor medical emergencies for visitors to the Myrtle Beach area. There are two facilities, on in the Little River area, and the other in Murrells Inlet. The Quality Assurance Department wishes to compare mean waiting times for patients in two locations. Samples of waiting times, reported in minutes follow:

Location Waiting time
Little River 31.73 28.77 29.53 22.08 29.47 18.60 32.94 25.18 29.82 26.49
Murrells Inlet 22.93 23.92 26.92 27.20 26.44 25.62 30.61 29.44 23.09 23.10 29.69 22.31

Assume the population standard deviations are not the same. At the .05 significance level, is there a difference in the mean waiting time?

Exercise 52

The president of the American Insurance Institute wants to compare the yearly costs of auto insurance offered by two leading companies. He selects a sample of 15 families, some with only a single insured driver, others with several teenage drivers, and pays each family a stipend to contact the two companies and ask for a price quote. To make the data comparable , certain features, such as the deductible amount and limits of liability, are standardized. The sample information is reported below. At the .01 significance level, can we conclude that there is a difference in the amounts quoted?

Family Progressive Car Insurance GEICO Mutual Insurance
Becker \$2,090 \$1,610
Berry \$1,683 \$1,247
Cobb \$1,402 \$2,327
Debuck \$1,830 \$1,367
Dubrul \$930 \$1,461
Eckroate \$697 \$1,789
German \$1,741 \$1,621
Glasson \$1,129 \$1,914
King \$1,018 \$1,956
Kucic \$1,881 \$1,772
Meredith \$1,571 \$1,375
Obeid \$874 \$1,527
Price \$1,579 \$1,767
Phillips \$1,577 \$1,636
Tresize \$860 \$1,188

#### Solution Preview

Exercise 27:
A recent study focused on the number of times men and women who live alone buy take-out in a month. The information is summarized below

Statistic Men Women
Sample Mean 24.51 22.69
Population Standard Deviation 4.48 3.86
Sample Size 35 40

At the .01 significance level, is there a difference in the mean number of times men and women order take out dinners in a month? What is the p-value?

The null hypothesis tested is

H0: There is no significance difference in the average number of times men and women who live alone buy take-out dinner. (µ1= µ2)

The alternative hypothesis is

H1: There is significance difference in the average number of times men and women who live alone buy take-out dinner. (µ1&#8800; µ2)

The test statistic used is

Rejection criteria: Reject the null hypothesis, if the calculated value of z is greater than the critical value of z at 0.01 significance level.

Details

Z Test for Differences in Two Means

Data
Hypothesized Difference 0
Level of Significance 0.01
Population 1 Sample
Sample Size 35
Sample Mean 24.51
Population Standard Deviation 4.48
Population 2 Sample
Sample Size 40
Sample Mean 22.69
Population Standard Deviation 3.86

Intermediate Calculations
Difference in Sample Means 1.82
Standard Error of the Difference in Means 0.972589328
Z-Test Statistic 1.871293411

Two-Tailed Test
Lower Critical Value -2.575829304
Upper Critical ...

#### Solution Summary

The solution provides step by step method for the calculation of test statistic for mean. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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