2. The drug Ritalin is designed to stimulate the central nervous system. In a random sample of 242 boys aged ten to twelve years old, it was found that 68 of the boys were taking Ritalin. It is known that the proportion of all boys aged 13 to 15 who take Ritalin is 22%. A researcher claims that the population proportions of boys who take Ritalin aged 10 to 12 is different than boys aged 13 to 15. Can you support this claim at the 5% significance level?a. Conduct a hypothesis test to test the claim at the 5% significance level. Be sure to state your Ho and Ha, your test statistic and p-value, whether or not you reject Ho and whether you support the claim.b. Write a complete sentence describing what a Type I error is in context.c. Write a complete sentence describing what a Type II error is in context.

Given Information: Sample size n=242 Number of successes x=68 Hypothesized value of population proportion is p0=0.22 (a) State the hypotheses as follows: Null Hypothesis H0:p=0.22 i.e., population proportion of boys who take Ritalin aged 10-12 is equal to that of boys aged 13-15. Alternative Hypothesis Ha:p≠0.22 i.e., population proportion of boys who take Ritalin aged 10-12 is different from that of boys aged 13-15 (claim). The test statistic is given by the formula: z=p^-p0p01-p0n where, p^ is the sample proportion computed as follows: p^=xn=68242=0.2809917355≈0.28099 Substitute the values in the formula: z=p^-p0p01-p0n=0.28099-0.220.221-0.22242=0.060990.02662876094≈2.29 Thus, the value of the test statistic is 2.29 P-value is obtained using Excel function "=1-NORM.S.DIST(2.29,TRUE)". The value obtained is 0.011011. Since this a two-tailed test, multiply the value by 2 i.e., 2×0.011011≈0.022 Since the p-value (0.022) is less than the significance level (0.05), reject H0. Therefore, at 5% significance level, there is enough evidence to support the claim that population proportion of boys who take Ritalin aged 10-12 is different than that boys aged 13-15. (b) Type I error is the probability of rejecting the null hypothesis when it is actually true. In the given context, type I error occurs when it is concluded that population proportion of boys who take Ritalin aged 10-12 is different from that of boys aged 13-15, when in fact the population proportion of boys who take Ritalin aged 10-12 is is equal to that of boys aged 13-15. (c) Type II error is the probability of failing to reject the null hypothesis when it is actually false. In the given context, type II error occurs when it is concluded that population proportion of boys who take Ritalin aged 10-12 is equal to the proportion of boys who take Ritalin aged 13-15, when in fact the population proportion of boys who take Ritalin aged 10-12 is is different to that of boys aged 13-15.