Question

A particular paperback book is published in a choice of four different covers. A certain bookstore keeps copies of each cover on its racks. To test the hypothesis that sales are equally divided among the four choices, a random sample of 100 purchases is identified. a. If the resulting $X^{2}$ value were $6.4$, what conclusion would you reach when using a test with significance level .05? b. What conclusion would be appropriate at significance level $.01$ if $X^{2}=15.3 ?$ c. If there were six different covers rather than just four, what would you conclude if $X^{2}=13.7$ and a test with $\alpha=.05$ was used?

          A particular paperback book is published in a choice of four different covers. A certain bookstore keeps copies of each cover on its racks. To test the hypothesis that sales are equally divided among the four choices, a random sample of 100 purchases is identified.
a. If the resulting $X^{2}$ value were $6.4$, what conclusion would you reach when using a test with significance level .05?
b. What conclusion would be appropriate at significance level $.01$ if $X^{2}=15.3 ?$
c. If there were six different covers rather than just four, what would you conclude if $X^{2}=13.7$ and a test with $\alpha=.05$ was used?

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Added by Lauren H.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Madhur L

06/21/2023

Step 1

For a chi-square test with 4 covers, the degrees of freedom (df) would be $4 - 1 = 3$. At a significance level of 0.05, we can find the critical value from the chi-square distribution table, which is $\chi^2_{0.05,3} = 7.815$. Since the calculated $X^2 = 6.4$ is Show more…

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A particular paperback book is published in a choice of four different covers. A certain bookstore keeps copies of each cover on its racks. To test the hypothesis that sales are equally divided among the four choices, a random sample of 100 purchases is identified. a. If the resulting $X^{2}$ value were $6.4$, what conclusion would you reach when using a test with significance level .05? b. What conclusion would be appropriate at significance level $.01$ if $X^{2}=15.3 ?$ c. If there were six different covers rather than just four, what would you conclude if $X^{2}=13.7$ and a test with $\alpha=.05$ was used?

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