Prof. Smith claims that less than 5% of his students fail his statistics course.
ID: 3135031 • Letter: P
Question
Prof. Smith claims that less than 5% of his students fail his statistics course. He chooses a random sample of 400 students and decides that he will accept the claim only if less than 16 of the 400 students fail his course. In fact his claim is true - the actual percentage of students who fail is 4.5%; nevertheless the sample had 22 students who failed. Based on the sample data Prof. Smith would make a error with probability. Type I ;.05 Type II ;.3156 Type I ;.5689 Type II ;.6844 None of the above A study is to be conducted to determine whether the mean cost of membership in a gym is more than $300. A random sample of 49 gyms is selected and the following decision rule is constructed: do not reject the null hypothesis if the sample mean is less than or equal to $315, otherwise reject the null hypothesis. The standard deviation of gym membership cost is known from historical evidence to be $40. What is the beta-risk if the population mean cost is actually $305?.5987.9599.9236.0401 None of the aboveExplanation / Answer
1. Prof Smith claims...
He did not reject Ho, so this is a type II error.
Hence, we find the probability that he gets at least 16 students who fail.
We first get the z score for the critical value:
x = critical value = 16
u = mean = np = 18
s = standard deviation = sqrt(np(1-p)) = 4.146082488
Thus, the corresponding z score is
z = (x-u)/s = -0.48
Thus, the right tailed area is
P(z > -0.48 ) = 0.6844 [ANSWER, D]
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