In your opinion, how safe is the food you buy? CBS News polled 1048 U.S. adults

Question

In your opinion, how safe is the food you buy? CBS News polled 1048 U.S. adults and asked them the following question: Overall, how confident are you that the food you buy is safe to eat. Very confident, somewhat confident, not too confident, not at all confident? The pie chart shows the responses to the question. You conduct a survey using the same equation. The contingency table shows the results of your survey classified by gender. Assuming the variables gender and response are independent, did the number of female respondents or male respondents exceed the expected number of "very confident" responses? Assuming the variables gender and response are independent, did the number of female respondents or male respondents exceed the expected number of "somewhat confident" responses? At alpha = 0.01, perform a chi-square independence test to determine whether the variables response and gender are independent. What can you conclude? In Exercises 4 and 5, perform a chi-square goodness-of-fit test to compare the distribution of responses shown in the pie chart with the distribution of your survey results for each gender. Use the distribution shown in the pie chart as the distribution. Use alpha = 0.05. Compare the distribution of responses by with the expected distribution. What can conclude? Compare the distribution of responses by with the expected distribution. What can conclude? In addition to the variables used in the Case what other variables do you think are to consider when studying the U.S. consumers' attitudes about food safety

Explanation / Answer

3. From the given data, the observed frequencies are

H0: The Variables Respones and Gender are indepedent

H1: The Variables Respones and Gender are not indepedent

Let the LOS be alpha = 5%

The expected frequencies are

The chisquare contribution values are

Degrees of freedom: 3

Test Statistic, X^2: 26.7114
Critical X^2: 7.8147
P-Value: 0.0000

Here Chisquare value 26.7114 > Chisquare critical value 7.814 and P value < alhpa 0.05, So we reject H0

Thus we conclude that the Variables Respones and Gender are not indepedent

Gender Response Female Male Total Very Confident 96 160 256 Somewhat Confident 232 180 412 Not too confident 56 52 108 Not at all confident 12 4 16 Total 396 396 792

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