Question

A social psychologist randomly wants to understand where people get their political news. She randomly assigns 35 volunteers to two experimental groups. 18 of them received their news for a month through news networks whereas 17 received their news from social media. After a month they tested political knowledge. The news network group had a mean of 24 and a standard deviation of 2 whereas the social media group had a mean of 26 and a standard deviation of 6.

What kind of test is best fit for this problem?

B. One-sample t-test

C. Paired-samples t-test

D. Independent-samples t-test

What is the observed value and do you accept or reject null hypothesis?

Is it a one or two tailed test?

what is the effect size?

Answer 1

What kind of test is best fit for this problem?

Independent-samples t-test

Reason: Two samples compared for the attribute

Is it a one or two tailed test?

- Two tailed ( whether two network has the same mean or not ).

The provided sample means are shown below:

$\bar X_1 = 24$$\bar X_2 = 26$

Also, the provided population standard deviations are:

$\sigma_1 = 2$$\sigma_2 = 6$

and the sample sizes are n1 = 18 and n2 = 17.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: $\mu_1 = \mu_2$

Ha: $\mu_1 \neq \mu_2$

This corresponds to a two-tailed test, for which a z-test for two population means, with known population standard deviations, will be used.

(2) Rejection Region

Based on the information provided, the significance level is α = 0.05, and the critical value for a two-tailed test is z_c = 1.96.

(3) Test Statistics

The z-statistic is computed as follows:

$z = \frac{\bar X_1 - \bar X_2}{\sqrt{\sigma_1^2/n_1 + \sigma_2^2/n_2}}$

$z = \frac{ 24 - 26}{\sqrt{ 2^2/18 + 6^2/17}}$

z = -1.307

(4) Decision about the null hypothesis

Since it is observed that |z| = 1.307 < z_c = 1.96, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p = 0.1911, and since p = 0.1911 > 0.05, it is concluded that the null hypothesis is not rejected.