Question

A major automobile company claims that its New electric powered car has an average range of more that 100 miles. A random sample of 50 new electric cars was selected to test the claim. Assume that the population standard deviation is 12 miles. A 5% level of significance will be used for the test.

A) What would be the consequences of making a Type II error in this problem?

B) Compute the Probability of making a Type II error if the true population mean is 105 miles.

C) What is the maximum probability of making a Type I error in this problem?

Answer 1

a)
type II error occurs when one incorrectly fails to reject H0
Here, the conclusion made would be the average range of new electric car is not more than 100 miles though it is greater than 100 miles.

b)
Std. Error. SE = sigma/sqrt(n) = 12/sqrt(50) = 1.6971

for alpha of 0.05,
x-critical = 100 + 1.645*1.6971 = 102.7914

P(X>102.79|mu=105)
= P(z > (102.79 - 105)/1.6971)
= P(z > -1.3022)
= 0.9034

Hence type II error = 0.9034

C)
probability of making type I error = 0.05