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    Two -Sample Tests of Hypothesis

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    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

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

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    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.

    $2.19

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