Given two independent random samples with the following results:n1=13x‾1=186s1=33 n2=13x‾2=171s2=23Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed. Step 1 of 3 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Complete Question

Given two independent random samples with the following results:

Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed.

Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval.

Step 2 of 3: Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Step 3 of 3: Construct the 90% confidence interval. Round your answers to the nearest whole number.

Step 1 of 3:

Step 2 of 3:

Step 3 of 3:

Step-by-step explanation:

Now considering the Step 1 of 3, the  point estimate that should be used in constructing the confidence interval  is mathematically represented as  

=>    

=>    

Now considering the Step 2 of 3

Given that the confidence level is  90% then the level of significance is mathematically represented as

=>    

Generally the degree of freedom is mathematically represented as

=>    

=>  

From the student t-distribution table the critical value of   at a degree of freedom of  

Generally the pooled variance is mathematically represented as    

Generally the margin of error is mathematically represented as

=>    

=>    

Now considering the Step 3 of 3

Generally the 90% confidence interval is mathematically represented as

=>  

=>  

1. 3

2. 4

3. 1

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