(20) 9. It is believed that 23% or more of the student population of ABC College
ID: 2949550 • Letter: #
Question
(20) 9. It is believed that 23% or more of the student population of ABC College is over age 25, Suppose 98 students were randomly surveyed to see if at least 23% of the population speaks a language other than English at least 10 hours a week (5) A. What is the null hypothesis using symbols? What is the null hypothesis using words? (5) B. What is the alternate hypothesis using symbols? What is the alternate hypothesis using words? (4) C. State what would be true if there was a type I error. (o D State whar would be tnei herewas a pe I erer (2) E. Suppose the probability ofa type l error is l 190 and the probability of a type II eror is 8%. What is the power of the test?Explanation / Answer
Let 'p' denote the proportion of population that speak a language other than English at least 10 hours a week.
(a)
The null hypothesis is:
H0: p = 0.23
Null hypothesis: proportion of population that speak a language other than English at least 10 hours a week is equal to 0.23
(b)
The alternate hypothesis is:
Ha: p > 0.23
Null hypothesis: proportion of population that speak a language other than English at least 10 hours a week is greater than 0.23
(c)
Type 1 error is incorrect rejection of a true null hypothesis. In this case it means that we reach to a conclusion that p > 0.23, when in reality p = 0.23
(d)
Type 2 error is incorrectly retaining a false null hypothesis. In this case it means that we reach to a conclusion that p = 0.23, when in reality p > 0.23
(e)
Probability of making a type 1 error = Significance level, a = 0.11
Probability of making a type 2 error = 0.08
Power of test = 1 - (Probability of making a type 2 error) = 1-0.08 = 0.92
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