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    Hypothesis Testing Problems

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    31. A new weight-watching company, Weight Reducers International, advertises that those
    who join will lose, on the average, 10 pounds the first two weeks with a standard deviation
    of 2.8 pounds. A random sample of 50 people who joined the new weight reduction program
    revealed the mean loss to be 9 pounds. At the .05 level of significance, can we
    conclude that those joining Weight Reducers on average will lose less than 10 pounds?
    Determine the p-value.

    32. Dole Pineapple, Inc., is concerned that the 16-ounce can of sliced pineapple is being
    overfilled. Assume the standard deviation of the process is .03 ounces. The quality control
    department took a random sample of 50 cans and found that the arithmetic mean
    weight was 16.05 ounces. At the 5 percent level of significance, can we conclude
    that the mean weight is greater than 16 ounces? Determine the p-value.

    38. A recent article in The Wall Street Journal reported that the 30-year mortgage rate is now
    less than 6 percent. A sample of eight small banks in the Midwest revealed the following
    30-year rates (in percent):

    4.8 5.3 6.5 4.8 6.1 5.8 6.2 5.6

    At the .01 significance level, can we conclude that the 30-year mortgage rate for small
    banks is less than 6 percent? Estimate the p-value.

    27 A recent study focused on the number of times men and women who live alone buy
    take-out dinner 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?

    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, one in the Little
    River Area and the other in Murrells Inlet. The Quality Assurance Department wishes to
    compare the mean waiting time for patients at the two locations. Samples of the 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
    Murrell's Inlet 22.93 23.92 26.92 27.20 26.44 25.62 30.61 29.44 23.09 23.10 26.69 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?
    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 .10 significance level,
    can we conclude that there is a difference in the amounts quoted?
    BTW - this is a paired t test

    Progressive GEICO
    Family Car Insurance 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

    23 A real estate agent in the coastal area of Georgia wants to compare the variation in the
    selling price of homes on the oceanfront with those one to three blocks from the ocean.
    A sample of 21 oceanfront homes sold within the last year revealed the standard deviation
    of the selling prices was $45,600. A sample of 18 homes, also sold within the last
    year, that were one to three blocks from the ocean revealed that the standard deviation
    was $21,330. At the .01 significance level, can we conclude that there is more variation
    in the selling prices of the oceanfront homes?

    28 The following is a partial ANOVA table.

    Complete the table and answer the following questions. Use the .05 significance level.
    a. How many treatments are there?
    b. What is the total sample size?
    c. What is the critical value of F?
    d. Write out the null and alternate hypotheses.
    e. What is your conclusion regarding the null hypothesis?

    19. In a particular market there are three commercial television stations, each with its own
    evening news program from 6:00 to 6:30 P.M. According to a report in this morning's local
    newspaper, a random sample of 150 viewers last night revealed 53 watched the news
    on WNAE (channel 5), 64 watched on WRRN (channel 11), and 33 on WSPD (channel 13).
    At the .05 significance level, is there a difference in the proportion of viewers watching
    the three channels?

    20. There are four entrances to the Government Center Building in downtown Philadelphia.
    The building maintenance supervisor would like to know if the entrances are equally utilized.
    To investigate, 400 people were observed entering the building. The number using
    each entrance is reported below. At the .01 significance level, is there a difference in the
    use of the four entrances?

    Entrance Frequency
    Main Street 140
    Broad Street 120
    Cherry Street 90
    Walnut Street 50
    Total 400

    How do you classify statistical findings in order of power: nominal, ordinal, interval, and ratio?
    Give example by making up values.

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    Solution Summary

    The solution provides step by step method for the calculation of testing of hypothesis. 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.