Question

Don't argue Refer to Exercise 2. Yvonne finds that $96$ of the $150$ students $(64\%)$ say they rarely or never argue with friends. A significance test yields a $P$-value of$0.0291$ Interpret the $P$-value.

Short answer

There is a $2.91\%$ possibility that the proportion of students in the sample who say they never argue with friends is$0.64$or more extreme, when the proportion of all students who say they never argue with friends is $0.72$

Step-by-step solution

Step 1:Given information

Don't argue Refer to Exercise 2. Yvonne finds that$96$ of the $150$students $(64\%)$ say they rarely or never argue with friends. A significance test yields a $P$-value of $0.0291$

Step 2:Explaination

$P=0.0291=2.91\%$

$\hat{p}=64\%=0.64$

Claim is proportion is $72\%$

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is that the population mean is equal to the value given in the claim. If the null hypothesis is the claim, then the alternative hypothesis statement is the opposite of the null hypothesis.

$H_0:p=72\%=0.72$

$H_a:p\ne 0.72$

The P-value is the probability of getting the value of the test static or a value more extreme, when the null hypothesis is correct.

There is a $2.91\%$ possibility that the proportion of students in the sample who say they never argue with friends is$0.64$or more extreme, when the proportion of all students who say they never argue with friends is $0.72.$