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    One way ANOVA table and chi square statistics

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    An investigator for a consumer cooperative organized a study of the mileages obtainable from three different brands of gasoline. Using 15 identical motors set to run at the same speed, the investigator randomly assigned each brand of gasoline to 5 of the motors. Each of the motors was then run on 10 gallons of gasoline, with the total mileages obtained as follows.
    Gas 1 Gas 2 Gas 3
    220 244 252
    251 235 272
    226 232 250
    246 242 238
    260 225 256
    Test the hypothesis that average mileage obtained is the same for all three types of gasoline. Use 5% level of significance.

    During the first few weeks of the new television season, the evening news audience proportions were recorded as ABC- 31%, CBS- 34%, and NBC- 35%. A sample of 600 homes yielded the following viewing audience data.
    Program #homes
    ABC 150
    CBS 200
    NBC 250
    Determine whether or not there has been a significant change in the number of viewing audience of the three networks.

    a.State the null and alternative hypotheses to be tested.
    b.Compute the expected frequencies.
    c.Compute the test statistic.
    d. The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test. What do you conclude?
    e.Determine the p-value or its range and perform the test.

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    Solution Preview

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    Solution 1

    Ho: (Average mileage is same for all types of gasoline)
    Ho: (Average mileage is not same for all types of gasoline)

    Using One way ANOVA analysis on MS Excel at 5% level of significance, we get

    Anova: Single Factor

    Groups Count Sum Average Variance
    Column 1 5 1203 240.6 287.8
    Column 2 5 1178 235.6 59.3
    Column 3 5 1268 253.6 150.8

    Source of Variation SS df ...

    Solution Summary

    There are two problems. For first problem, solution describes the steps in detemining whether different brands of gasoline have any significant effect on mileage. One way ANOVA analysis is carried out.

    For second problem, solution explains the steps in calculating chi square statistics with the help of observed and expected frequencies. Finally this statistics is compared with critical value to determine whether there has been a significant change in viewing audience for given channels.