Chapter 9.1, Problem 14E

(a)

To determine

The mean for the hemoglobin present per deciliter blood to cause risk of anemia.

Answer to Problem 14E

There is a chance of 0.16% of obtaining a sample mean of 11.3 gram per deciliter of blood or more whenthe population mean is equal to 12.

Explanation of Solution

Given Information:

Population mean $\overline{x}=11.3$

Number of sample $n=50$

New population value $p=0.0016$

Standard deviation $s=1.6$

Population proportion valueis 0.0016. Convert 0.0016 into percentage.

  $0.0016\times 100=0.16\%$

From exercise 4 population mean valueis 12.

Thus, null hypotheses $H_o:\mu =12$ .

Alternative hypotheses $H_a:\mu <12$ .

Hence, if the population mean is equal to 12, then there is a chance of 0.16% of obtaining a sample mean of 11.3 gram per deciliter of blood 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 14E

There is enough convincing evidence against the null hypothesis when $\alpha$ value is 0.05 or 0.01.

Explanation of Solution

From 13(a), population proportion is 0.0016. 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 $p=0.0016<0.01$ .

Thus, $H_o$ is rejected.

Hence, when $\alpha$ value is 0.05 or 0.01 there is enough convincing evidence against the null hypothesis.