# Standard Deviation and Confidence Interval Solve

**Topics:**Standard deviation, Normal distribution, Confidence interval

**Pages:**2 (389 words)

**Published:**April 21, 2015

Question 1 of 1:

Interpreting the Confidence Interval

Solve the following problems:

A simple random sample of 40 salaries of NCAA football coaches has a mean of $415,953 and a standard deviation of $463,364. Construct a 95% confidence interval estimate of the mean salary of an NCAA football coach. In a study designed to test the effectiveness of acupuncture for treating migraine, 142 subjects were treated with acupuncture and 80 subjects were given a sham treatment. The numbers of migraine attacks for the acupuncture treatment group had a mean of 1.8 and a standard deviation of 1.4. The numbers of migraine attacks for the sham treatment group had a mean of 1.6 and a standard deviation of 1.2. Construct the 95% confidence interval estimate of the mean number of migraine attacks for those treated with acupuncture. Construct the 95% confidence interval estimate of the mean number of migraine attacks for those given a sham treatment. Compare the two confidence intervals. What do the results suggest about the effectiveness of acupuncture? Submission Requirements:

Submit the assignment in a Microsoft Word or Excel document. Show detailed steps and provide appropriate rationale with your answers. Evaluation Criteria:

Correctly answered each question

Included appropriate steps or rationale to determine the answer to each question

Question 1 answer:

n = 40

x-bar = 415953

sd = 463364

z_c = 1/96 at 95% confidence.

Margin of error, E = (sd*z_c)/sqrt(n)

= (463364*1.96)/sqrt(40)

= 143597.99

95% CI = (415953 – 143497.99, 415953 + 143597.99)

= (272355.01, 559550.99)

Question 2 answer:

Let X be a random variable denoting the numbers of migraine attacks for the acupuncture treatment group Assume X follows a normal distribution with mean mu and standard deviation sig Sample mean of 142 subjects for X i.e. xbar=1.8

sample standard deviation for X i.e. s =1.4

Test statistic-> sqrt(n)*(xbar - mu)/s

which follows a t distribution with...

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