Question

Consider the estimated equation from Example 4.3, which can be used to study the effects of skipping class on college GPA: 2 colGPA 1.39 .412 hsGPA .015 ACT .083 skipped (.33) (.094) (.011) (.026) n 141, R2 .234. (i) Using the standard normal approximation, find the 95% confidence interval for hsGPA. (ii) Can you reject the hypothesis H0: hsGPA .4 against the two-sided alternative at the 5% level

Answer 1

Answer:

Step-by-step explanation:

1) The confidence interval is calculated as the following

$CI = ( \bar x-1.96 \sigma ,\bar x=1.96 \sigmam)$

$= (0.412-1.96 \times 0.094, 0.412 = 1.96 \times 0.094)\\\\= (0.22776, 0.59624)$

Hence, the confidence interval is $0.22776 \leq \beta_G_P_A \leq 0.59624)$

11) Under two sid t-tailed test, the null hypothesis

$H_0; \beta_{GPA}=0.4$

Against the alternative hypothesis

$H_1 ; \beta _{GPA} \neq 0.4$

Under null hypothesis

$t = \frac{\hat \beta _1 - \beta _1}{Se( \beta _1)} \\\\ =\frac{0.412-0.4}{0.094} \\\\=0.12766$

The degree of freedom is n - 1 = 140

From the t - table at 5% level of significance under two - tail is 1.96

Since , calculated value is lowe than the tabulated value, we do not reject the null hypothesis.