Test test the claim that the proportion of children from the low income group that did well on the test is

different than the proportion of the high income group. Test at the $0\mathrm{.}01$ significance level.

We are given that $23$ of $40$ children in the low income group did well, and $10$ of $35$ did in the high income

group.

a$)$ If we use $L$ to denote the low income group and $H$ to denote the high income group, identify the

correct alternative hypothesis.

$H_1$:${}_L>{}_H$

$H_1$:${}_L<msub\; id="EditorElement\_48616"><mrow><mi\; id="EditorElement\_48609"></mi></mrow><mrow\; id="EditorElement\_48615"><mi\; id="EditorElement\_48612">H</mi></mrow></msub>$

$H_1$:$p_L=p_H$

$H_1$:$p_L{p}_H$

b$)$ The test statistic value is:

c$)$ Using the P$-$value method, the P$-$value is:

d$)$ Based on this, we

Reject $H_0$

Fail to reject $H_0$

e$)$ Which means

The sample data supports the rejection of the no group difference

There is sufficient evidence to warrant rejection of the alternative claim

There is not sufficient evidence to support the rejection of no group difference

There is not sufficient evidence to warrant rejection of the alternative claim