# 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

https://brainmass.com/statistics/hypothesis-testing/two-sample-tests-of-hypothesis-276241

#### 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?

Answer

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≠ 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.