A researcher wants to test if the average annual income of residents in a city is $50,000. He randomly surveys 100 residents from the city. Assuming the sample has an average annual income of $52,000 with a standard deviation of $10,000, which type of hypothesis test should the researcher use?A.A. Two-sample t-testB.B. Paired sample t-testC.C. One-sample t-testD.D. Chi-square test
Question
A researcher wants to test if the average annual income of residents in a city is 52,000 with a standard deviation of $10,000, which type of hypothesis test should the researcher use?A.A. Two-sample t-testB.B. Paired sample t-testC.C. One-sample t-testD.D. Chi-square test
Solution
The researcher should use C. One-sample t-test.
Here's why:
A one-sample t-test is used when you want to know if your sample comes from a particular population. In this case, the researcher is trying to determine if the average annual income of residents in a city is $50,000, which is a specific population value.
Option A, a two-sample t-test, is used when comparing the means of two independent groups to determine if they are different from each other. In this case, there is only one group (residents of the city), so a two-sample t-test would not be appropriate.
Option B, a paired sample t-test, is used when comparing the means of the same group at two different times. In this case, there is no time factor involved, so a paired sample t-test would not be appropriate.
Option D, a Chi-square test, is used when dealing with categorical data. In this case, the data is numerical (annual income), so a Chi-square test would not be appropriate.
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