Final answer:
The correct answer is option d. Z-test.When comparing two independent sample means with known population variances, the Z-test is used.
Step-by-step explanation:
When comparing the means of two independent samples with known population variances, the appropriate statistical test is the Z-test. This situation corresponds to option (b) which is a test of two independent means. Since the population standard deviations are known, and we are testing the means, the Z-test is used instead of a T-test, which is more suitable when population standard deviations are unknown. The random variable in this case would be the difference between the sample means. The Z-test uses the standard normal distribution to determine if there is a significant difference between the sample means.
The appropriate statistical test for comparing the means of two independent samples, assuming that the population variances are known, is the Z-test.
Is this a test of two means or two proportions? This is a test of two means.
Are the population standard deviations known or unknown? The population variances are known.
Which distribution do you use to perform the test? You use the normal distribution to perform the Z-test.
What is the random variable? The random variable in this test is the difference between the means of the two independent samples.