Q.12 - The Practice of Statistics for AP

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.

Step-by-Step Solution

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 1: introduction

Given,

sample size is $150$

population value is $72\%$

new population value is 0.0291

Step 2: 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 $0.72$.

Step 3: 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