# Test of hypothesis, Confidence Interval

1) Recruit 25 volunteers who have received a medication and find they have a mean concentration of 7 with a standard deviation of 2. Assume normally distributed.

FIND: 95% CONFIDENCE INTERVAL for pop mean concentration

Find: 99% confidence interval for pop var of conc

HOW large a sample is needed to ensure the length of the CI in prob 1 is 0.5.

2.

100 hypertensive people are given z drug that is effective on 20 people. Effective=there blood pressure is lowered by at least 10.

6.54 What is the standard error of d?

6.55 What is the 95% confidence interval for the pop mean of d?

6.56 Can we make a statement about the effectiveness of this drug?

6.57 What does a 95% confidence interval mean in words

https://brainmass.com/statistics/confidence-interval/test-hypothesis-confidence-interval-28462

#### Solution Preview

Problem 1

Recruit 25 volunteers who have recieved a medication and find they have a mean concentration of 7 with a standard deviation of 2. Assume normall ditributed.

FIND: 95% CONFIDENCE INTERVAL for pop mean concentration

Find: 99% confidence interval for pop var of conc

HOW large a sample os needed to ensure the length of the CI in prob 1 is 0.5.

FIND: 95% CONFIDENCE INTERVAL for pop mean concentration

Mean=M = 7

Standard deviation =s= 2

sample size=n= 25

sx=standard error of mean=s/square root of n= 0.4 = ( 2 /square root of 25)

Confidence level= 95%

Therefore Significance level=alpha (a) = 5% =100% -95%

No of tails= 2

Since sample size= 25 < 30

and we are estimating population standard deviation from the sample use t distribution

t at the 0.05 level of significance and 24 degrees of freedom (=n-1) and 2 tail= 2.0639

Upper confidence limit= M +t*sx= 7.8256 =7+2.0639*0.4

Lower confidence limit= M -t*sx= 6.1744 =7-2.0639*0.4

Confidence interval is between 6.174 and 7.8256

Find: 99% confidence interval for pop var of conc

sample size=n= 25

standard deviation =s= 2

Variance =s 2 = 4 =2 ^2

We use the chi square distribution for the confidence interval for the variance

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#### Solution Summary

The expert provides a test of hypothesis and confidence intervals. How large a sample is needed to ensure the length is calculated.