Part 2 of 2
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Suppose that a poll taken 10 years ago found that $64 \%$ of parents spank their children. Suppose a recent poll of 450 adults with children finds that 257 indicated that they spank their children. Assuming parents' attitude toward spanking has not changed since the original poll, how many of the 450 parents surveyed would be expected to spank their children? Do the results of the survey suggest that parents' attitude toward spanking may have changed since the original poll? Why?
We would expect 288 parents to spank their children.
(Round to the nearest whole number as needed)
Do the results of the survey suggest that parents' attitude toward spanking may have changed since the original poll? Choose the correct answer below.
A. No, 257 is within one standard deviation of the expected number of adults who spank
B. No, 257 is within two standard deviations of the expected number of adults who spank
C. Yes, 257 is more than two standard deviations from the expected number of adults who spank
D. Yes, 257 is less than the expected amount of adults that spank their children.
Answer
Therefore, the answer to the second part of the question is \(\boxed{\text{'B. No, 257 is within two standard deviations of the expected number of adults who spank'}}\).
Step 1 ：Given that a poll taken 10 years ago found that 64% of parents spank their children, we can calculate the expected number of parents who would spank their children based on this percentage. This is done by multiplying the total number of parents surveyed (450) by the percentage of parents who spank their children according to the original poll (64%).
Step 2 ：\(450 \times 0.64 = 288\)
Step 3 ：The expected number of parents who spank their children is \(\boxed{288}\).
Step 4 ：In the recent poll, 257 out of 450 adults indicated that they spank their children. We compare this actual number with the expected number to determine if parents' attitude toward spanking may have changed since the original poll.
Step 5 ：The standard deviation of the expected number of parents who spank their children is approximately 10.18. The actual number of parents who spank their children (257) is more than one standard deviation but less than two standard deviations away from the expected number.
Step 6 ：Therefore, the answer to the second part of the question is \(\boxed{\text{'B. No, 257 is within two standard deviations of the expected number of adults who spank'}}\).
