A survey was conducted in a large city to investigate public opinion on banning the use of trans fats in restaurant cooking. A random sample of 230 city residents with school-age children was selected, and another random sample of 341 city residents without school-age children was also selected. Of those with school-age children, 94 opposed the banning of trans fats, and of those without school-age children, 147 opposed the banning of trans fats. An appropriate hypothesis test was conducted to investigate whether there was a difference between the two groups of residents in their opposition to banning of trans fats. Is there convincing evidence of a difference between the two population proportions at the significance level of 0.05? (A) Yes, because the sample proportions are different. (B) Yes, because the probability of observing a difference at least as large as the sample difference is greater than 0.05. (C) Yes, because the probability of observing a difference at least as large as the sample difference, if the two population proportions are the same, is less than 0.05. (D) No, because the probability of observing a difference at least as large as the sample differences, if the two population proportions are the same, is greater than 0.05. (E) No, because the probability of observing a difference at least as large as the sample difference is less than 0.05.
A survey was conducted in a large city to investigate public opinion on banning the use of trans fats in
restaurant cooking. A random sample of 230 city residents with school-age children was selected, and another
random sample of 341 city residents without school-age children was also selected. Of those with school-age
children, 94 opposed the banning of trans fats, and of those without school-age children, 147 opposed the
banning of trans fats. An appropriate hypothesis test was conducted to investigate whether there was a
difference between the two groups of residents in their opposition to banning of trans fats. Is there convincing
evidence of a difference between the two population proportions at the significance level of 0.05?
(A) Yes, because the sample proportions are different.
(B) Yes, because the
than 0.05.
(C) Yes, because the probability of observing a difference at least as large as the sample difference, if the two
population proportions are the same, is less than 0.05.
(D) No, because the probability of observing a difference at least as large as the sample differences, if the two
population proportions are the same, is greater than 0.05.
(E) No, because the probability of observing a difference at least as large as the sample difference is less than
0.05.
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