# Standard Deviations, Mean, Confidence Intervals, Margin of Error, and Linear Correlation

1. In a study designed to the test the effectiveness of magnets for treating back pain, 40 patients were given a treatment with magnets and also a sham treatment without magnets. Pain was measured using a scale from 0 (no pain) to 100 (extreme pain). After given the magnet treatments, the 40 patients had pain scores with a mean of 6.0 and a standard deviation of 2.6. After being given the sham treatments the 40 patients had pain scores with a mean of 7.8 and a standard deviation of 2.2.

b) Construct the 90% confidence interval estimate of the mean pain score for patients given sham treatment.

What is the confidence interval estimate of the population mean µ?

___< µ<____

2. Assume that a random sample is used to estimate a population p. Find the margin of error E that corresponds to the given statistics and confidence level. N=550, x=275, 90% confidence.

The margin of error E=____

3. Listed below are the budgets (in millions of dollars) and the gross receipts (in millions of dollars) for randomly selected movies.

Budget (x) 65 94 47 40 191 103 90

Gross (y) 64 69 43 54 567 141 44

a. Find the value of the linear correlation coffiecient r.

R=____(critical values for correlation coefficient table attached)

#### Solution Preview

Hi there,

Thanks for letting me work on your post. I've included my explanations in the word document.

1. In a study designed to the test the effectiveness of magnets for treating back pain, 40 patients were given a treatment with magnets and also a sham treatment without magnets. Pain was measured using a scale from 0(no pain) to 100 (extreme pain). After given the magnets treatments, the 40 patients had pain scores with a mean of ...

#### Solution Summary

The mean, confidence intervals, margin of errors and linear correlations are examined. The confidence interval estimate of the population means are given.