Question

Don’t argue Refer to Exercises 2 and 12.

a. What conclusion would you make at the $\alpha =0.01$ level?

b. Would your conclusion from part (a) change if a $5\%$ significance level was used

instead? Explain your reasoning.

Short answer

a. The evidence is present that percentage of teens in school that claim that they never argue with friends is different from $72\%$

b. From the given condition here, the conclusion is changed.

Step-by-step solution

Given Information

It is given that $P=0.0291=2.91\%$

$\alpha =0.01$

Proportion is$72\%$

To find the conclusion at α=0.01 level

Claim can be null of alternative hypothesis.

Null Hypothesis is the population proportion is value given in claim. Alternative hypothesis is opposite of null hypothesis.

$H_0:p=72\%=0.72$

$H_1:p\ne 0.72$

If $p\mathrm{value}<\alpha$, null hypothesis is rejected.

$0.0291<0.01\Rightarrow \text{Fail to reject}{H}_0$

Hence, the evidence is present that percentage of teens in school that claim that they never argue with friends is different from $72\%$

If above conclusion changed if 5% significance level is used

If significance level is $5\%=0.05$

Here $0.0291<0.05,\mathrm{reject}{H}_0$

The conclusion is changed.