Question

Refer to Exercise 2. For Yvonne's survey, 96 students in the sample said they rarely or never argue with friends. A significance test yields a P-value of 0.0291.

(a) Interpret this result in context.

(b) Do the data provide convincing evidence against the null hypothesis? Explain.

Short answer

a. Chance that students in the sample said rarely or never argue with friends is$0.0291$

b. Yes, the data provide convincing evidence against the null hypothesis

Step-by-step solution

introduction

Given,

sample size is $150$

population value is$72\%$

new population value is 0.0291

explanation part (a)

Calculating the null and alternative hypotheses,

we get,

$\begin{array}{r}{H}_o:p=0.72\\ H_a:p\ne 0.72\end{array}$

The chance that students in the sample said rarely or never argue with friends is $0.0291$ if the population proportion is$0.72$.

explanation part (b)

The null hypothesis is not accepted as the value of p is less than the significant level of $5\%$or$0.05$

But $p=0.0291$which is less than $0.05$.

Yes, the data provide convincing evidence against the null hypothesis