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Depression and insomnia often go hand in hand Mendoza Company a national pharmaceutical firm has positioned itself as a specialist in the production of both antidepressants and sleeping pills Mendoza s current business model describes the following breakdown of America s approximately 50 million adults suffering from insomnia 17 use both antidepressants and sleeping pills regularly 24 use only antidepressants regularly 15 use only sleeping pills regularly and the remaining 44 use neither antidepressants nor sleeping pills regularly In a recent study on insomnia in a psychiatry journal 160 American adults suffering from insomnia but otherwise chosen at random were asked about their use of antidepressants and sleeping pills The breakdown of their answers is given by the top row of numbers in the table below These numbers are the frequencies observed for the sample of 160 insomniacs The second row of numbers gives the expected frequencies under the hypothesis that Mendoza s model is correct The bottom row of numbers contains the following value for each of the categories of medication use So E JE Part 1 Fill in the missing values in the table Round your responses for the expected frequencies to two or more decimal places Round your Jo JE responses to three or more decimal places Send data to Excel Observed frequency fo Observed frequency Expected frequency Expected frequency Expected frequency JE Both 29 0 Only antidepressants 31 38 40 1 426 Only sleeping pills 19 0 0 Neither Total a Determine the type of test statistic to use 81 70 40 1 596 160 Part 2 Answer the following to summarize the test of the hypothesis that Mendoza s model is correct Use the 0 10 level of significance for the test Type of test statistic Choose one b Find the value of the test statistic Round your answer to two or more decimal places 0 c Find the critical value Round your answer to two or more decimal places d Can we conclude that the percentages given in Mendoza s model are incorrect 19 B M

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