In order to compare the means of the populations, independent random samples of 400observations are selected from each population, with the following results:1.Sample 1Sample 25,2755,2402 200S1 150Use a 95% confidence interval to estimate the difference between the population meansa.(u1-12). Interpret the confidence interval.b. Test the null hypothesis Ho: (H1 H2)0 versus the alternative hypothesisHai (11-12) # 0, Give the significance level of the test and interpret the result.c. suppose the test in part b was conducted with the alternative hypothesis Ha: (μ1-μ2) > 0.How would your answer to part b change?Test the null hypothesis Ho: (4-2,-25 vs Ha: (11-Ha) # 25, Give the significanced.level and interpret the result. Compare your answer to the test conducted in part b.What assumptions are necessary to ensure the validity of the inferential procedures appliede.in parts a-d?

Question
Asked May 29, 2019
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Part A, B, C

In order to compare the means of the populations, independent random samples of 400
observations are selected from each population, with the following results:
1.
Sample 1
Sample 2
5,275
5,240
2 200
S1 150
Use a 95% confidence interval to estimate the difference between the population means
a.
(u1-12). Interpret the confidence interval.
b. Test the null hypothesis Ho: (H1 H2)0 versus the alternative hypothesis
Hai (11-12) # 0, Give the significance level of the test and interpret the result.
c. suppose the test in part b was conducted with the alternative hypothesis Ha: (μ1-μ2) > 0.
How would your answer to part b change?
Test the null hypothesis Ho: (4-2,-25 vs Ha: (11-Ha) # 25, Give the significance
d.
level and interpret the result. Compare your answer to the test conducted in part b.
What assumptions are necessary to ensure the validity of the inferential procedures applied
e.
in parts a-d?
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In order to compare the means of the populations, independent random samples of 400 observations are selected from each population, with the following results: 1. Sample 1 Sample 2 5,275 5,240 2 200 S1 150 Use a 95% confidence interval to estimate the difference between the population means a. (u1-12). Interpret the confidence interval. b. Test the null hypothesis Ho: (H1 H2)0 versus the alternative hypothesis Hai (11-12) # 0, Give the significance level of the test and interpret the result. c. suppose the test in part b was conducted with the alternative hypothesis Ha: (μ1-μ2) > 0. How would your answer to part b change? Test the null hypothesis Ho: (4-2,-25 vs Ha: (11-Ha) # 25, Give the significance d. level and interpret the result. Compare your answer to the test conducted in part b. What assumptions are necessary to ensure the validity of the inferential procedures applied e. in parts a-d?

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Expert Answer

Step 1

Here, the population standard deviation is unknown, so the t-distribution is used.

It is provided that n1 = n2 = 400.

The required assumptions are:

Two population variances are equal and the population data follows normal distribution.

 

a.

The formula to calculate the 95% confidence interval for the difference between the two population means is:

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Step 2

The calculations are shown below:

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Step 3

Thus, the 95% confidence interval to estimate the ...

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