Consider the following data from two independent samples with equal population variances. Construct a 90% confidence interval to estimate the difference in population means. Assume the population variances are equal and that the populations are normally distributed.

- [tex]x_1 = 36.3[/tex], [tex]x_2 = 32.3[/tex]
- [tex]s_1 = 8.5[/tex], [tex]s_2 = 9.2[/tex]
- [tex]n_1 = 18[/tex], [tex]n_2 = 19[/tex]

Question

High School

We appreciate your visit to Consider the following data from two independent samples with equal population variances Construct a 90 confidence interval to estimate the difference in population means Assume. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Answer :

lana676 lana676 · Answer 1 · 2023-11-10T02:10:08-05:00

The 90% confidence interval for the difference in population means is (-0.541, 8.541).

Calculate the difference in sample means, standard error, critical value, margin of error, and construct the confidence interval.

Constructing a 90% Confidence Interval for the Difference in Population Means

To construct a 90% confidence interval for the difference in population means, we can use the formula:

CI = (x1 - x2) ± (Zα/2) × √((s12/n1) + (s22/n2))

Calculate the difference in sample means: x1 - x2 = 36.3 - 32.3 = 4.0

Calculate the standard error: √((s12/n1) + (s22/n2)) = √((8.52/18) + (9.22/19)) ≈ 2.761

Find the critical value, Zα/2, for a 90% confidence level (α = 0.10) = 1.645

Calculate the margin of error: (Zα/2) × standard error = 1.645 × 2.761 ≈ 4.541

Construct the confidence interval: 4.0 ± 4.541 = (-0.541, 8.541)

The 90% confidence interval for the difference in population means is (-0.541, 8.541).

To Learn more about Confidence Interval here:

https://brainly.com/question/34700241

#SPJ11