A researcher administers a treatment to a sample of participants selected from a population with µ = 80.If the researcher obtains a sample mean of M = 88,given the same alpha level,which combination of factors is most likely to result in rejecting the null hypothesis?
A)σ = 5 and n = 25
B)σ = 5 and n = 50
C)σ = 10 and n = 25
D)σ = 10 and n = 50

Question

A researcher administers a treatment to a sample of participants selected from a population with µ = 80.If the researcher obtains a sample mean of M = 88,given the same alpha level,which combination of factors is most likely to result in rejecting the null hypothesis?​
A)​σ = 5 and n = 25
B)​σ = 5 and n = 50
C)​σ = 10 and n = 25
D)​σ = 10 and n = 50

Quizplus · Accepted Answer

A larger sample size (n = 50) will increase the power of the test, making it more likely to detect a significant difference between the sample mean and population mean. A smaller standard deviation (σ = 5) will also make the sample mean more significantly different from the population mean, further increasing the power of the test. Therefore, the combination of a smaller σ and larger n (option B) is the most likely to result in rejecting the null hypothesis.

A Researcher Administers a Treatment to a Sample of Participants