Inferring about population Means
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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 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.
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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 ...
Education
- BEng (Hons) , Birla Institute of Technology and Science, India
- MSc (Hons) , Birla Institute of Technology and Science, India
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