Question 8.304

3. The Mozart Effect. A random sample of 45 children showed a mean increase of 7 IQ points after listening to a Mozart piano sonata for about 10 minutes. The distribution of such increases is unknown, but the standard deviation is assumed to be 2 IQ points.

  1. Find the point estimate of the increase in IQ points for all children after they have listened to Mozart.
  2. Calculate
  3. Find for a confidence interval with 90% confidence.
  4. Compute and interpret the margin of error for a confidence interval with 90% confidence.
  5. Construct and interpret a 90% confidence interval for the mean increase in IQ points for all children after listening to a Mozart piano sonata for about 10 minutes.

8.99.3

(a) 7 points (b) 0.2981 point (c) 1.645 (d) 0.4904 point. We can estimate to within 0.4904 point with 90% confidence. (e) (6.5096, 7.4904). We are 90% confident that the true mean increase in IQ points for all children after listening to a Mozart piano sonata for about 10 minutes lies between 6.5106 points and 7.4904 points.