A researcher is conducting a matched-pairs study.She gathers data on each pair in the study resulting in: $$\begin{array} { | c | c | c | }
\hline \text { Pair } & \text { Group 1 } & \text { Group 2 } \
\hline 1 & 10 & 12 \
\hline 2 & 8 & 9 \
\hline 3 & 11 & 11 \
\hline 4 & 8 & 10 \
\hline 5 & 9 & 12 \
\hline
\end{array}$$ Assume that the data are normally distributed in the population.The level of significance is selected to be 0.10.If the alternative hypothesis is that the average difference is greater than zero, the null hypothesis would be rejected if the observed value of t is _______.
A)greater than 1.533
B)less than -1.533
C)greater than 2.132
D)less than -2.132
E)equal to 2.333

Question

A researcher is conducting a matched-pairs study.She gathers data on each pair in the study resulting in: $$\begin{array} { | c | c | c | } 
\hline \text { Pair } & \text { Group 1 } & \text { Group 2 } \
\hline 1 & 10 & 12 \
\hline 2 & 8 & 9 \
\hline 3 & 11 & 11 \
\hline 4 & 8 & 10 \
\hline 5 & 9 & 12 \
\hline
\end{array}$$ Assume that the data are normally distributed in the population.The level of significance is selected to be 0.10.If the alternative hypothesis is that the average difference is greater than zero, the null hypothesis would be rejected if the observed value of t is _______.
A)greater than 1.533
B)less than -1.533
C)greater than 2.132
D)less than -2.132
E)equal to 2.333

Quizplus · Accepted Answer

In a matched-pairs study, the null hypothesis typically states that there is no difference between the pairs, or that the average difference is zero. When the alternative hypothesis is that the average difference is greater than zero, we are conducting a one-tailed t-test. Given the level of significance is 0.10, and assuming the degrees of freedom (df) for this test is 4 (n-1, where n is the number of pairs), the critical value from the t-distribution table for a one-tailed test with df=4 at the 0.10 level is approximately 1.533. Therefore, to reject the null hypothesis, the observed value of t must be greater than 1.533.

A Researcher Is Conducting a Matched-Pairs Study Assume That the Data Are Normally Distributed in the Population