Question

Given two independent random samples with the following results:

n
1
​
=11
x
ˉ

1
​
=174
s
1
​
=34
​

n
2
​
=8
x
ˉ

2
​
=191
z
2
​
=22
​
Use this data to find the 90 क्ष contidence 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 2 of 3 : Find the margh of error to be used in construxting the confidence interval, Rosind your answer to sic tiecimvilaces. Answer How to enter youranswer (ogerd in new window?

Answer 1

To find the margin of error for constructing a confidence interval, you need to calculate the standard error and multiply it by the appropriate critical value from the t-distribution. In this case, the margin of error is approximately 27.09.

Step-by-step explanation:

To find the margin of error for constructing a confidence interval, we first need to calculate the standard error. The formula for the standard error of the difference between two sample means is:

SE = sqrt((s1^2/n1) + (s2^2/n2))

where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes. In this case, we have:

SE = sqrt((34^2/11) + (22^2/8))

SE ≈ 14.82

The margin of error is then obtained by multiplying the standard error by the appropriate critical value from the t-distribution, depending on the desired level of confidence. Since the problem specifies a 90% confidence interval, we use a critical value of t = 1.833 for the two-sample case.

Margin of Error = t * SE

Margin of Error ≈ 1.833 * 14.82 ≈ 27.09