Hey Can you help me solve this question Suppose that we would like to determine
ID: 3134956 • Letter: H
Question
Hey Can you help me solve this question
Suppose that we would like to determine if the average traffic flow at an intersection in the city is greater than 50 cars per minute. A set of 49 one-minute observation intervals over a one-week period was randomly selected and the average traffic flow was observed to be 47.60 carsminute. Assume that the standard deviation is known to be 7 cars/minute. (a) Using a 0.02 level of significance, would you reject the hypothesis that the average traffic flow is greater than 50 cars/minute? What is the Type I error? (b) If the true average traffic flow is 48 cars/minute, with the test in (a), what is the Type II error? (The probability that we will not reject the hypothesis that the average traffic flow is greater than 50 cars/minute).Explanation / Answer
A)
We need to test the null H0 : µ = 50 against the one-sided alternative H1 : µ <50, at level = 0.02. Since n = 49 , which is large, we will do a large-sample z-test. The rejection region is Z < z = -2.32, using the normal table.
Z = (X µ0) /(S/ n) = (47.6 50)/ 7/ 49 = -2.4 Since Z = -2.4 < 2.32, H0 is rejected. Thus, there is significant evidence at 2% signifi- cance level that the mean number of flow of cars is less then 50.
type 1 error will be incorrect rejection of the null hypothesis that the mean is greater than 50 instead of it being true.
b)
We need to test the null H0 : µ = 50 against the one-sided alternative H1 : µ <50, at level = 0.02. Since n is large, we will do a large-sample z-test. The rejection region is Z < z = -2.32, using the normal table.
Z = (X µ0) /(S/ n) = (48 50)/ (7 49) = -2. Since Z = -2. > -2.32, H0 is accepted. Thus, there is significant evidence at 2% signifi- cance level that the mean number of ccars is less than 50.
type 2 error will be when we fail to reject the null hypothesis that there are more than 50 cars instead of it being wrong.