Q.11 - The Practice of Statistics for AP

Question

Refer to Exercise 1. In Simon’s SRS, 16 of the students were left-handed. A significance test yields a P-value of 0.2184.

(a) Interpret this result in context.

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

Step-by-Step Solution

Answer

a. When the population proportion is$0.12$there is$0.2184$chance of having $16$or more left-handed students

b. No

Step 1: Explanation part (a)

We have,

sample size n = $100$

population value p =$0.2184$

old population value p  = $0.12$

Calculating the null and alternative hypotheses,

   $\begin{array}{r}{H}_o:p=0.12\\ H_a:p\ne 0.12\end{array}$

When the population proportion is $0.12$ there is $0.2184$ chance of having $16$ or more left-handed students.

Step 2: explanation part (b)

The null hypothesis is not valid if p value is less than $10\%$ or $0.1$

We know, p = $0.2184$ which is greater than$0.1$

Hence the data does not provide convincing evidence against the null hypothesis as it cant be removed.