Question 3

please write code in R

A 2022 survey of high school students found that a reported 14.1% of students used e-cigarettes. Researchers

attempting to show that the proportion of students using e-cigarettes has decreased in 2023. They take a sample of

189 high school students and find that 19 of the high school students used e-cigarettes.

Researchers use this sample to conduct a hypothesis test to determine if there is evidence that less students are

using e-cigarettes than the previous year. They plan to test their hypothesis at the \alpha =5% level.

Your answers should be exact, utilizing the binomial distribution.

a) Based on the proposed hypothesis test of the researcher, what is the assumed value of the population parameter

p. Save your answer in the variable q3.a

b) How many standard deviations (or standard errors) away from the mean is the observed sample proportion?

Save your answer in the variable q3.b

c) What is the probability under the null hypothesis of observing an estimate of the parameter as or more extreme

than the observed p?(This is the p-value). Save your answer in the variable q3.c

d) What is the maximum number of students reporting using e-cigarettes that would lead the researchers to reject

the null hypothesis? (The sample size remains unchanged). Save your answer in the variable q3.d

e) What is the exact probability of committing a type 1(type I) error if the null hypothesis is true? Save your

answer in the variable q3.e

A much larger study of high school students found that 10.0% of students used e-cigarettes. Assume this is the

true value of the parameter.

f) Based on the true value of the parameter, what is the probability of committing a type 1(type I) error? Save

your answer in the variable q3.f

g) Based on the true value of the parameter, what is the probability of observing a level of e-cigarette use that

would causes the researchers to reject the null hypothesis? (This is the power of the test). Save your answer

in the variable q3.g