Questions: Suppose that a poll taken 10 years ago found that 65% of parents spank their children. Suppose a recent poll of 500 adults with children finds that 293 indicated that they spank their children. Assuming parents' attitude toward spanking has not changed since the original poll, how many of the 500 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 parents to spank their children.
(Round to the nearest whole number as needed.)
Transcript text: Suppose that a poll taken 10 years ago found that $65 \%$ of parents spank their children. Suppose a recent poll of 500 adults with children finds that 293 indicated that they spank their children. Assuming parents' attitude toward spanking has not changed since the original poll, how many of the 500 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 $\square$ parents to spank their children.
(Round to the nearest whole number as needed.)
Solution
Solution Steps
Step 1: Calculate the Expected Number of Individuals Exhibiting the Behavior
To calculate the expected number of individuals \(E\) exhibiting the behavior or preference based on the historical percentage \(P_h\), we use the formula:
\[E = \frac{P_h}{100} \times N\]
Substituting the given values: \(P_h = 65\%\), \(N = 500\), we get:
\[E = \frac{65}{100} \times 500 = 325\]
Step 2: Analyze the Change in Behavior or Preference
The actual number of individuals \(X = 293\) is lower than the expected \(E = 325\), suggesting a potential decrease in the behavior or preference.
Final Answer:
Based on the recent poll, there appears to be a decrease in the behavior or preference compared to historical data.