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)

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.

Calculate the correlation of the data set (3,2), (3,3), (6,4).
A 95% confidence interval for the average miles per gallon for all cars of a ginven type is 32.1 plus/minus 1.8. The interval is based on a sample of 40 randomly selected cars.
What units represent the margin of error?
Suppose you want to decrease the margin of

Generate 50 random samples of size 10 from the file MBA and compute a 90% confidence interval for the mean of for each sample using the known population standard deviation of 3.831. Determine how many confidence intervals actually contain the true population mean of 14.77

Random sampling from two normal populations produced the following results:
Xbar1= 63, s1= 18 n1=50
xbar2= 60 s2 = 7 n2 = 45
a. Estimate with 90% confidence the difference between the two population means.
b. Repeat part a changing the sample standard deviations to 41 and 15 respectively.
c. What happens when the s

I need to modify the data set to show If the time of month has any correlation to the amount of days people are absent. You can skew the numbers one way or another but I need a completed data set. The data set will be used for:
- Calculate coefficient of correlationand coefficient of determination.
- Develop a single linear

1. 12 mature citrus trees of one variety and 15 of another gave means andstandard deviations of their heights as 13.8 and 12.9 ft (means), and 1.2 and 1.5 ft (standard deviations).
Find a 95% confidence interval for the true difference in average heights between all trees of the first and the second variety.
Would you be able

A researcher is interested in determining the average number of years employees of a company stay with the company. If past information shows a standard deviation of 7 months, what size sample should be taken so that at 95% confidence the margin of error will be 2 months or less?"

1. In random samples of 25 from each of two normal populations, we found the following statistics:
x1 bar = 524 s1 = 129
x2 bar = 469 s2 = 131
a) estimate the difference between the two population means with 95% confidence.
b) repeat part a) increasing the standard deviations of s 1 to 255 and s 2 to 260.
c) describe what h

"In order to estimate the average time spent on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one week period. Assume the population standard deviation is 1.8 hours. With a 0.95 probability, the margin of error is approximately."