Chapter 9.1, Problem 13E

(a)

To determine

The population mean for students attitude towards the school and study habits.

Answer to Problem 13E

There is a chance of 1.01% of obtaining a sample mean of 125.7 or more when the population mean is equal to 115.

Explanation of Solution

Given Information:

Population mean $\overline{x}=125.7$

Number of sample $n=45$

New population value $p=0.0101$

Standard deviation $s=29.8$

Population proportion valueis 0.0101. Convert 0.0101 into percentage.

  $0.0101\times 100=1.01\%$

From exercise 3 population mean valueis 115.

Thus, null hypotheses $H_o:\mu =115$ .

Alternative hypotheses $H_a:\mu >115$ .

Hence, if the population mean is equal to 115, then there is a chance of 1.01% of obtaining a sample mean of 125.7 or more.

(b)

To determine

Explain whether the null hypothesis can be reject or not when $\alpha$ value is 0.05 or 0.01.

Answer to Problem 13E

When $\alpha =0.05$ there is enough convincing evidence against the null hypothesis and when $\alpha =0.01$ there is not enough convincing evidence against the null hypothesis.

Explanation of Solution

From 13(a), population proportion is 0.0101. If p value is smaller than significant level of 0.05 and 0.01, then the null hypothesis is rejected.

p value when $\alpha =0.05$

  $p=0.0101<0.05$

Thus, $H_o$ is rejected.

For $\alpha =0.01$ , p value $p=0.0101>0.01$ .

Thus, $H_o$ cannot be rejected.

Hence, when $\alpha =0.05$ there is enough convincing evidence against the null hypothesis and when $\alpha =0.01$ there is not enough convincing evidence against the null hypothesis.