A manufacturer claims that the average lifetime of its lightbulbs is equal to 36 months. A random sample of 64 bulbs has a mean lifetime of 32 months, and the sample standard deviation is 11 months. We will be using a z-test for the population mean at α = 0.05 to check the manufacturer’s claim.
A critical value for this test is:
1.645
1.96
2.31
2.821
The critical value for a z-test with α = 0.05 is 1.96.
To find the critical value, we need to determine the z-score that corresponds to an area of 0.05 in the tails of the standard normal distribution.
The critical value is found by subtracting 0.05 from 1 and then dividing by 2 (since the area is divided equally between the two tails). This gives us 0.475.
Using a standard normal distribution table or a calculator, we find that the z-score corresponding to an area of 0.475 is approximately 1.96.
Therefore, the critical value for this test is 1.96.