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.
The test statistic is:
2.91
2.12
-2.12
-2.91
The test statistic can be calculated using the formula:
test statistic = (sample mean - population mean) / (sample standard deviation / √sample size)
In this case, the sample mean is 32 months, the population mean is 36 months, the sample standard deviation is 11 months, and the sample size is 64. Plugging these values into the formula:
test statistic = (32 - 36) / (11 / √64)
= -4 / (11 / 8)
= -32 / 11
The test statistic is approximately -2.91.
Therefore, the correct answer is:
-2.91