Researchers have selected a simple random sample of size n = 12 from a population for the purpose of testing the null hypothesis H₀: $\mu$ = $\mu$₀ against the alternative hypothesis H_a: $\mu$ $\mu$₀.Studies indicate that a substantial degree of skewness can be expected in the population from which the sample was obtained.What might the researchers consider doing in this situation? A)There really isn't anything they can do;they simply have to proceed with what the data give them. B)They might proceed as usual but alter the P-value later to compensate for the skewness in their data. C)They might use a test procedure that doesn't require Normality,such as a sign test using the median. D)They might apply a transformation to the data,such as a logarithm,to try to achieve symmetry. E)C and D are each possible approaches they might consider using.

Question

Researchers have selected a simple random sample of size n = 12 from a population for the purpose of testing the null hypothesis H₀: $\mu$ = $\mu$₀ against the alternative hypothesis H_a: $\mu$> $\mu$₀.Studies indicate that a substantial degree of skewness can be expected in the population from which the sample was obtained.What might the researchers consider doing in this situation? A)There really isn't anything they can do;they simply have to proceed with what the data give them. B)They might proceed as usual but alter the P-value later to compensate for the skewness in their data. C)They might use a test procedure that doesn't require Normality,such as a sign test using the median. D)They might apply a transformation to the data,such as a logarithm,to try to achieve symmetry. E)C and D are each possible approaches they might consider using.

Quizplus · Accepted Answer

When dealing with a sample that is expected to be skewed, it is best to consider non-parametric approaches for testing hypotheses. Option C suggests using a sign test which does not require normality assumptions. Option D suggests transforming the data, which can help to achieve symmetry and may allow for the use of parametric tests that require normality assumptions. Therefore, the best choice in this situation is to consider using both the sign test and transforming the data, making option E the correct answer.

Researchers Have Selected a Simple Random Sample of Size N μ\muμ

Researchers Have Selected a Simple Random Sample of Size N $\mu$