Question

ONLY QUESTIONS D, E, F and G

Question 3: Independent Samples t-Test Group Statistics bype of school Mean reading score public private 168 32 51.8452 54.2500 SM Deviation 10.42279 9 19677 Sid Error Mean 0414 162578 Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means 95% Confidence Mean Sid. Error Interval of the Sig. 2. Differenc Differenc Difference o tailed) Lower Upper 564 453 1.217 198 225 -2.40476 1.97519 -6.29986 1.49034 reading Equal variances assumed score Equal variances -1.326 47.49 191 -2.40476 1.81377 -6.05260 124308 not assumed a. What was the independent variable in this analysis? b. What was the dependent variable in this analysis? c. Describe both samples (using the given statistics). d. What are the null and alternative hypotheses for this study? e. Can you assume equal variances based on Levene's Test? f. Write out the appropriate t-test formula using the numbers given in the output. Make sure to write out the original formula in symbols before putting in the numbers. 8. Complete Hypothesis Test Step 4. i. Decision about null hypothesis? ii. is it significant? lii. Sentence iv. APA style

Answer 1

D)

Here we wan to test that mean of public and private school have same reading score or not
Let $\small \mu_1$ be the population mean of public school reading score

and $\small \mu_2$ be the population mean of private  school reading score

Then our Hypothesis will be:

$\small H_0:\mu_1 - \mu_2 = 0$

$\small H_1:\mu_1 - \mu_2 \neq 0$

So it is a two tailed test.

E)

Now before applying t test for independent test we need to check that whether both the population come form same population or not.

Hypothesis:

$\small H_0:\sigma_1^2 / \sigma_1^2 =1$

$\small H_1:\sigma_1^2 / \sigma_1^2 \neq 1$

So for that test is conducted above and as we can see that p value corresponding to that test is 0.453

So here P value = 0.453 > $\small \alpha = 0.05$

which implies that here we do not have enough evidence to reject null hypothesis.

So it implies that both the populations have same population variances.

So here we will apply t test for independent t test with equal variances.

F)

So here t statistic is given by:

$\small t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \sim t_{n_1+n_2-2}$

So t statistic is -1.217

and it will follow t distribution with 198 df

corresponding p value is 0.225

P value = 0.225

G)

Since here we can see that p value = 0.225 > $\small \alpha = 0.05$

which implies that here we do not have enough evidence to reject null hypothesis.

which implies that mean of both the public and private schools reading score are same.

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