## Related questions with answers

A statistics instructor wanted to see if student participation in review preparation methods led to higher examination scores. Five students were randomly selected and placed in each test group for a three-week unit on statistical inference. Everyone took the same examination at the end of the unit, and the resulting scores are shown. Is there sufficient evidence at $\alpha=0.05$ to conclude an interaction between the two factors? Is there sufficient evidence to conclude a difference in mean scores based on formula delivery system? Is there sufficient evidence to conclude a difference in mean scores based on the review organization technique?

Formulas provided | Student-made formula cards | |
---|---|---|

Student-led review | 89,76,80,90,75 | 94,86,80,79,82 |

Instructor-led review | 75,80,68,65,79 | 88,78,85,65,72 |

If the null hypothesis is rejected, use Scheffe's test when the sample sizes are unequal to test the differences between the means and use the Tukey test when the sample sizes are equal. For these exercises, perform these steps. Assume the assumptions have been met.

a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results.

Solution

VerifiedWe have two factors, $A$ and $B$. Factor $A$ is designated as the review organization technique, whereas factor $B$ is the type of formula delivery system.

The hypotheses for the interaction between $A$ and $B$ are:

$H_{0}:$ There is no interaction effect between factor $A$ and factor $B$.

$H_{1}:$ There is an interaction effect between factor $A$ and factor $B$.

The hypotheses for $A$ are:

$H_{0}:$ There is no difference in mean scores based on the review organization technique.

$H_{1}:$ There is a difference in mean scores based on the review organization technique.

The hypotheses for $B$ are:

$H_{0}:$ There is no difference in mean scores based on the formula delivery system.

$H_{1}:$ There is a difference in mean scores based on the formula delivery system.

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