Question

Stating hypotheses

a. A change is made that should improve student satisfaction with the parking situation at a local high school. Before the change, $37\%$of students approve of the parking that's provided. The null hypothesis $\mathrm{H}0:\mathrm{p}>0.37H_0:p>0.37$is tested against the alternative Ha: $\mathrm{p}=0.37H_a:p=0.37$

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

$\text{H0:}{x}^{-}=3000{\text{grams}}^{-5}{H}_0:\overline{x}=3000\text{grams}$

Ha: ${\mathrm{x}}^{-}<3000$grams $H_a:\overline{x}<3000$grams

explain what's wrong with the stated hypotheses. Then give correct hypotheses.

Short answer

The correct hypotheses are listed as:

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

Part (b)$H_0:p=0.3000\text{grams}$, $H_a:p<0.3000\text{grams}$

Step-by-step solution

Part (a) Step 1:Given information

$\text{The null hypothesis}\mathrm{H}0:\mathrm{p}>0.37H_0:p>0.37\text{is tested against the alternative}$

$\text{Ha:}\mathrm{p}=0.37H_a:p=0.37$

Part (b) Step 2:Explaination

The null hypothesis given by the following expression:

$H_0:\hat{p}=0.37$

And the alternate hypothesis is given by the following expression:

$H_a:\hat{p}\ne 0.37$

Now, know that the hypotheses always used the population value not the sample value. So the sample values stated in the null hypothesis and alternate hypothesis should be remove and replaced by population value.

$\text{The correct hypotheses are listed as:}$

$H_0:p=0.37$

$H_a:p>0.37$

Hence, there is use population value not the sample value in hypotheses.

Part (b)Step 2:Given information

$\mathrm{H}0:{\mathrm{x}}^{-}=3000\text{grams}{H}_0:\overline{x}=3000\text{grams}$

$\text{Ha:}{\mathrm{x}}^{-}<3000\text{grams}{H}_a:\overline{x}<3000\text{grams}$

Part (b) Step 2:Explaination

The null hypothesis given by the following expression:

$H_0:\overline{x}=0.3000\text{grams}$

And the alternate hypothesis is given by the following expression:

$H_a:\overline{x}<0.3000\text{grams}$

Now, know that the hypotheses always used the population value not the mean value. So the sample values stated in the null hypothesis and alternate hypothesis should be remove and replaced by population value.

$\text{The correct hypotheses are listed as:}$

$H_0:p=0.3000\text{grams}$

$H_a:p<0.3000\text{grams}$

Hence, there is use population value not the sample value in hypotheses.