Question

Stating hypotheses

a. A change is made that should improve student satisfaction with the parking situation at your school. Before the change, $37\%$of students approve of the parking that's provided. The null hypothesis $\mathrm{H}0:{\mathrm{p}}^{\wedge =0.37}{H}_0:\hat{p}=0.37$is tested against the alternative Ha: ${\mathrm{p}}^{\wedge >0.37}{H}_a:\hat{p}>0.37$

b. A researcher suspects that the mean birth weights of babies whose mothers did not see a doctor before delivery is less than 3000 grams. The researcher states the hypotheses as

$\mathrm{H}0:\mu =3000\text{grams}{H}_0:\mu =3000\text{grams}$

$\text{Ha:}\mu \le 2999\text{grams}{H}_a:\mu \le 2999\text{grams}$

Short answer

The appropriate hypotheses are:

Part (a)$H_0:p=0.37$,$H_a:p>0.37$

Part (b)$H_1:p>0.50$,$H_a:\mu <3000$

Step-by-step solution

Part (a)Step 1:Given information

$\mathrm{H}0:\mu =3000\text{grams}{H}_0:\mu =3000\text{grams}$

$\text{Ha:}\mu \le 2999\text{grams}{H}_a:\mu \le 2999\text{grams}$

Part (a) Step 2:Explaination

Inequalities are shown in the null hypothesis not the alternative hypothesis. Here, inequality has been provided in the alternative hypothesis and value of the parameter must be same in both the parameters. So, it is required to replace 2999 by 3000

$\text{The hypotheses are:}$

$H_0:\mu =3000$$H_a:\mu <3000$