Chapter 9.2, Problem 1.1CYU

To determine

To check: Whether there is sufficient evidence to conclude that actual figures of the proportions are higher at high school.

Answer to Problem 1.1CYU

No, there is sufficient evidence to conclude that actual figures of the proportions are higher at high school.

Explanation of Solution

Given:

Confidence level = 95%

Number of respondents (n) = 250

Number of respondents that has sent images ( x ) = 63

Population proportion ( p ) = 0.20

Formula used:

The test statistic formula is:

  $z=\frac{\widehat{p}-p_0}{\sqrt{\frac{p_0\left(1-p_0\right)}{n}}}$

Calculation:

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:p=0.20\\ H_a:p>0.20\end{array}$

The obtained Ti-83 output is:

  

The p -value (0.0199) is greater than the significance level. The decision is the non-rejection of null hypothesis. Thus, at 5% significance level there is insufficient evidence to conclude that actual figures of the proportions are higher at high school.