Acompany that receives shipments of batteries tests a random sample of nine of them before agreeing to take a shipment. the company is concerned that the true mean lifetime for all batteries in the shipment should be at least 50 hours. from past experience it is safe to conclude that the population distribution of lifetimes is normal with a standard deviation of 3 hours. for one particular shipment the mean lifetime for a sample of nine batteries was 48.2 hours.

a. test at the 10% level the null hypothesis that the population mean lifetime is at least 50 hours.
b. find the power of a 10%-level test when the true mean lifetime of batteries is 49 hours.

We conclude that the mean lifetime of batteries is less than 50 hours.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 50 hours

Sample mean, = 48.2 hours

Sample size, n = 9

Alpha, α = 0.10

Population standard deviation, σ = 3 hours

a) First, we design the null and the alternate hypothesis

We use One-tailed z(left) test to perform this hypothesis.

Formula:

Putting all the values, we have

Now,

Since,  

We reject the null hypothesis and accept the alternate hypothesis.

Thus, we conclude that the mean lifetime of batteries is less than 50 hours.

b) Power of the test

constants mean the stopped points or the points on a graph that nothing is changing, hope this

step-by-step explanation: