Math / Data & Statistics

QuestionSydnel Thomas $11 / 22 / 244.00 \mathrm{PM}$ Question 5 of 20 mileste20 pint(0) possiblo Thil question $\mathrm{I}_{\text {polnt(s) possib- }}$ Submil test
Find the standardized lest statistic, $L$ , to test the claim that $\mu_{1}>\mu_{2}$ . Two samples are randomly selected and come from populations that are normat. The samplo statistics are given below Aasume that $\sigma_{1}^{2} \neq \sigma_{2}^{2}$ . $n_{1}=18, n_{2}=13, \bar{x}_{1}=485, \bar{x}_{2}=470, s_{1}=40, s_{2}=25$

Studdy Solution

STEP 1

1. The samples are independent and come from normally distributed populations.
2. The population variances are not equal ( $\sigma_1^2 \neq \sigma_2^2$ ).
3. We are using a two-sample t-test to compare the means.

STEP 2

1. Calculate the standard error of the difference between the sample means.
2. Compute the test statistic $L$ .

STEP 3

Calculate the standard error of the difference between the sample means using the formula:
$SE = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$
Substitute the given values:
$SE = \sqrt{\frac{40^2}{18} + \frac{25^2}{13}}$
Calculate each term:
$\frac{40^2}{18} = \frac{1600}{18} \approx 88.89$
$\frac{25^2}{13} = \frac{625}{13} \approx 48.08$
Add these values:
$SE = \sqrt{88.89 + 48.08} = \sqrt{136.97} \approx 11.70$

STEP 4

Compute the test statistic $L$ using the formula:
$L = \frac{\bar{x}_1 - \bar{x}_2}{SE}$
Substitute the given values:
$L = \frac{485 - 470}{11.70} = \frac{15}{11.70} \approx 1.28$
The standardized test statistic $L$ is:
$\boxed{1.28}$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms