Question

10) (1 point) A manufacturer of electronic kits has found that the mean time required for novices to assemble its new circuit tester is 2.7 hours, with a standard deviation of 0.8 hours. A consultant has developed a new instructional booklet intended to reduce the time an inexperienced kit builder will need to assemble the device and the manufacturer needs to decide whether or not to send out the new booklet.

The testable hypotheses in this situation are H0:μ=2.7H0:μ=2.7 vs HA:μ<2.7HA:μ<2.7.

1. Identify the consequences of making a Type I error.
A. The manufacturer sends out a helpful instructional booklet.
B. The manufacturer does not send out a helpful instructional booklet.
C. The manufacturer sends out an unhelpful instructional booklet.
D. The manufacturer does not send out an unhelpful instructional booklet.

2. Identify the consequences of making a Type II error.
A. The manufacturer sends out an unhelpful instructional booklet.
B. The manufacturer does not send out a helpful instructional booklet.
C. The manufacturer sends out a helpful instructional booklet.
D. The manufacturer does not send out an unhelpful instructional booklet.

To monitor the assembly time of inexperienced kit builders using the booklet, the manufacturer is going to take a random sample of 10 novices and calculate the mean time to assemble the circuit tester. If it is less than 2.6, they will send out the new instructional booklet. Assume the population standard deviation is 0.8 hours.

3. What is the probability that the manufacturer will make a Type I error using this decision rule? Round your answer to four decimal places.

4. Using this decision rule, what is the power of the test if the actual mean time to assemble the circuit tester is 2.1 hours? That is, what is the probability they will reject H0H0 when the actual average time is 2.1 hours? Round your answer to four decimal places.

Answer 1

type i error - when we reject the null hypothesis even when null hypothesis is true
type ii error- when we fail to reject the null hypothesis, even when null hypothesis is false

1)
type i error is to conclude that mu < 2.7
hence
option A) The manufacturer sends out a helpful instructional booklet.

2)
type ii error- fail to conclude mu < 2.7
B. The manufacturer does not send out a helpful instructional booklet.

3)
mu - z *sigma/sqrt(n) = 2.6
2.7 - z * 0.8/sqrt(10) = 2.6
z = 0.395

alpha = 0.3463