# Inferring about population Means

In random samples of 12 from each of two normal populations, we found the following statistics:

Xbar1 = 74 S1= 18

Xbar2 = 71 S2 =16

a) Test with α= .05 to determine whether we can infer that the population means differ.

b) Repeat part a increasing the standard deviations to S1= 210 and S2 =198.

c) Describe what happens when the sample standard deviations get larger.

d) Repeat part a with samples of size 150.

e) Discuss the effects of increasing the sample size.

f) Repeat part a changing the mean of sample 1 to Xbar1 = 76.

g) Discuss the effect of increasing Xbar1.

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Solution

In random samples of 12 from each of two normal populations, we found the following statistics:

Xbar1 = 74 S1= 18

Xbar2 = 71 S2 =16

a) Test with α= .05 to determine whether we can infer that the population means differ.

Since sample size is less than 30, but samples are from normal population, we will use z statistics

Here

Standard Error can be calculated as under

Observed value of Z is calculated as under

It's a two tailed test

Critical value of Z is (-1.96, 1.96) from the tables of normal distribution

Since ...

#### Solution Summary

Solution describes the steps in hypothesis testing about population means from two sample statistics. Result are studied with variation in sample means, sample deviation and sample sizes.