Chapter 9.2, Problem 55E

Solution

a)

The parameter of interest.

Given:Let “ p” be the proportion of U.S teens aged 13 to 17 thought that young people should wait to have sex until marriage.

The Minitab output of the results of a significance test and 95% confidence interval based on survey as shown below

  

Explanation:

A parameter is any summary number, which describes for entire population. Here the population is all teens of U.S aged 13 to 17. The parameter of interest is the proportion of teens aged 13 to 17 who thinkthat young people should wait to have sex until marriage.

b)

To verify the conditions for performing the significance test are met in this case.

Concept used:The conditions to satisfy to run one sample Z test

1) The sample should be random

2) np = 10

3) n(1-p) = 10

4) There should be at least 10% of people of population in the sample.Calculation:

The U.S teens aged 13 to 17 are selected in a sample randomly.Let p₀be the proportion of U.S teens aged 13 to 17who think that young people should wait to have sex until marriage.

  $p_0=0.56$

The sample size = n = 439

  $\begin{array}{l}n{p}_0=439*0.56=245.84\\ n{p}_0\ge 10\\ n(1-p_0)=439*(1-0.56)=193\\ n(1-p_0)\ge 10\end{array}$

We know that there will be at least 4390 teens who think that they should wait to have sex until marriage. So the 10% condition is satisfied.

Conlcusion:All the conditions for performing the significance test are met in this case.

c)

To interpret the p value.

Explanation:

The p value of the significance test is 0.011. This tell us that at an average 1.1% of the teens differ from the population of teens who think that they should wait to have sex until marriage.

d)

To check whether there is evidence that the actual population proportion differs from 0.5.

Explanation:

The 95% confidence interval is (0.513935, 0.606794) does not contain the true population proportion of p = 0.50. So at 5% level of significance there is sufficient evidence to conclude that actual population proportion of U.S teens aged 13 to 17 who think that they should wait to have sex untill marriage differ from 0.5.