Question

Five years? ago, 10.3?% of high school students had tried marijuana for the first time before the age of 13. A school resource officer? (SRO) thinks that the proportion of high school students who have tried marijuana for the first time before the age of 13 has increased since then. ?(a) Determine the null and alternative hypotheses. Which of the following is? correct? A. Upper H 0?: pequals0.103?; Upper H 1?: pgreater than0.103 B. Upper H 0?: pequals0.103?; Upper H 1?: pnot equals0.103 C. Upper H 0?: pequals0.103?; Upper H 1?: pless than0.103 ?(b) Suppose sample data indicate that the null hypothesis should not be rejected. State the conclusion of the researcher. A. There is sufficient evidence to conclude that the proportion of high school students has increased. B. There is not sufficient evidence to conclude that the proportion of high school students has stayed the same. C. There is not sufficient evidence to conclude that the proportion of high school students has increased. D. There is sufficient evidence to conclude that the proportion of high school students has stayed the same. ?(c) Suppose, in? fact, that the proportion of high school students who have tried marijuana before the age of 13 was 10.5?%. Was a type I or type II error? committed? A. The SRO committed a type II error because he accepted the null hypothesis when the alternative hypothesis is true. B. The SRO committed a type II error because he did not reject the null hypothesis when the alternative hypothesis is true. C. The SRO committed a type Upper I error because he did not reject the null hypothesis when the alternative hypothesis is true. D. The SRO committed a type Upper I error because he accepted the null hypothesis when the alternative hypothesis is true

Answer 1

(A)

Since we wnat to test whether  the proportion of high school students who have tried marijuana for the first time before the age of 13 has increased from 10.3%. The alternative hypothesis is:

The null hypothesis is:

(b)

Since null hypothesis is not rejected so

C. There is not sufficient evidence to conclude that the proportion of high school students has increased.

(c)

Since true proportion is 10.5% but we fail to reject the null hypothesis so we fail to reject the false null hypothesis. So type II error is possible.

B. The SRO committed a type II error because he did not reject the null hypothesis when the alternative hypothesis is true.