Which of the following hypothesis tests would be most appropriate to use, considering the following null hypothesis and sample details?Null hypothesis: The average access to basic water services of people in rural and urban areas is equal.Sample size: 7Unknown population standard deviationBoth samples are normally distributedA two-sample z-testAny parametric testA two-sample t-testAny non-parametric test
Question
Which of the following hypothesis tests would be most appropriate to use, considering the following null hypothesis and sample details?Null hypothesis: The average access to basic water services of people in rural and urban areas is equal.Sample size: 7Unknown population standard deviationBoth samples are normally distributedA two-sample z-testAny parametric testA two-sample t-testAny non-parametric test
Solution
A two-sample t-test would be the most appropriate to use in this scenario.
Here's why:
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The null hypothesis is comparing the averages of two different groups (rural and urban areas), which is a scenario typically handled by a two-sample test.
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The sample size is small (n=7), which is less than 30. This is a common rule of thumb for using a t-test instead of a z-test.
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The population standard deviation is unknown. A t-test is typically used when this is the case, as it is more conservative and does not require knowledge of the population standard deviation.
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Both samples are normally distributed. This is an assumption of the t-test, so it is appropriate to use it in this case.
Therefore, considering all these factors, a two-sample t-test is the most appropriate test to use.
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