Chapter 9.1, Problem 12E

(a)

To determine

The population of teens that never argue with their friends.

Answer to Problem 12E

There is a chance of 0.0291 of obtaining 96 students or more who said they never argue with friends in a sample of 150 students when the population proportion is equal to 0.72.

Explanation of Solution

Given Information:

Population value from exercise 2 $p=72\%$

Number of sample $n=150$

New population value $p=0.0291$

From exercise 1 population valueis 72%.

Convert 72% into decimal.

  $\frac{72}{100}=0.72$

Thus, null hypotheses $H_o:p=0.72$ .

Alternative hypotheses $H_a:p\ne 0.72$ .

Hence, if the population proportion is equal to 0.72, then there is a chance of 0.0291 of obtaining 96 students or morewho said they never argue with friends in a sample of 150 students.

(b)

To determine

Explain whether the data provide sufficient evidence against the null hypothesis.

Answer to Problem 12E

There is enough convincing evidence against the null hypothesis.

Explanation of Solution

From 12(a), null hypothesis is 0.72. If p value is smaller than significant level of 5%, then the null hypothesis is rejected.

Convert 5% into decimal.

  $\frac{5}{100}=0.05$

But $p=0.0291<0.05$ .

Thus, $H_o$ can be rejected.

Hence, there is enough convincing evidence against the null hypothesis.