Given to dependent random samples with the following results:Population 1: 83,72,64,61,72,74,72,66Population 2: 85,64,66,52,78,83,70,68Can it be concluded, from this data, that there is a significant difference between the two population means?Let d= ( population 1 entry)-( population 2 entry), use a significance level of a = 0.05 for the test. Assume that both population are normally distributed. 1. State the null and alternative hypothesis for the test.2. Find the value of the standard deviation of the paired differences. Round to one decimal place.3. Commute the value of the test statistic. Round to three decimal places.4. Determine the decision rule for rejecting the null hypothesis Ho. Round the numerical portion of your answer to three decimal places.

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Asked Apr 15, 2019
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Given to dependent random samples with the following results:

Population 1: 83,72,64,61,72,74,72,66

Population 2: 85,64,66,52,78,83,70,68

Can it be concluded, from this data, that there is a significant difference between the two population means?

Let d= ( population 1 entry)-( population 2 entry), use a significance level of a = 0.05 for the test. Assume that both population are normally distributed. 

1. State the null and alternative hypothesis for the test.

2. Find the value of the standard deviation of the paired differences. Round to one decimal place.

3. Commute the value of the test statistic. Round to three decimal places.

4. Determine the decision rule for rejecting the null hypothesis Ho. Round the numerical portion of your answer to three decimal places.

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Expert Answer

Step 1

Two dependent random samples are selected from a population and it is assumed that both populations are normally distributed. The level of significance for the test is α = 0.05.

The hypothesis test based on the data would be called a paired comparisons test. The difference between the pair of measurements is called di.

Step 2

Part (1): Null and alternative Hypothesis for the test:

Denote μ1 as the true mean of population 1 and μ2 as the true mean of population 2.

Let μd denote the difference between means of population 1 and population 2. That is,

μd = μ1 μ2.

The hypotheses appropriate for the test are as follows:

Null hypothesis:

H0: μd = 0; that is, there is no significant difference between two population means.

Alternate hypothesis:

H1: μd 0; that is, there is significant difference between two population means.

Step 3

Part (2): Finding the value of the standard deviation of the paired differences:

The difference between each pair observations is obtained as,

di = population 1 entry – population 2 entry for the i’th pair of observations.

In Excel, put population 1 data in column A and population 2 data in column B, without using column headings so that first pair of data is on line 1.

In cell C1, enter the formula, =A1 – B1. This calculates the difference, di, for t...

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