Question

We don't like to find broken crackers when we open the package. How can makers reduce breaking? One idea is to microwave the crackers for 30 seconds right after baking them. Analyze the results from two experiments intended to examine this idea. STATE: Does microwaving significantly improve indicators of future breaking? How large is the improvement? What do you conclude about the idea of microwaving crackers? (a) PLAN: The experimenter randomly assigned 65 newly baked crackers to be microwaved and another 65 to a control group that is not microwaved. Fourteen days after baking, 3 of the 65 microwaved crackers and 57 of the 65 crackers in the control group showed visible checking, which is the starting point for breaks.

SOLVE: The 95% confidence interval for the difference in proportions ?1−?2 is

−0.806±0.083 .

−0.831±0.079 .

−0.756±0.124

. −0.806±0.099 .

CONCLUDE: Select the correct conclusion based off of your confidence interval test results.

We are 95% confident that microwaving reduces the percentage of checked crackers by between 75.2% and 91.0% . We are 95% confident that microwaving reduces the percentage of checked crackers by between 63.2% and 88.0% . We are 95% confident that microwaving reduces the percentage of checked crackers by between 72.3% and 88.9% . We are 95% confident that microwaving reduces the percentage of checked crackers by between 70.7% and 90.5% .

(b) PLAN: The experimenter randomly assigned 20 crackers to be microwaved and another 20 to a control group. After 14 days, he broke the crackers. The table contains the summaries of the pressure needed to break them, in pounds per square inch. Microwave Control Mean 139.6 77.0 Standard deviation 33.6 22.6

SOLVE: To test whether microwaving significantly increases the pressure needed to break a cracker, we should use the following inference.

two samples, inference about mean

matched pairs, inference about proportions

two samples, inference about proportions

matched pairs, inference about mean

The test whether microwaving significantly increases the mean pressure needed to break a cracker, has ? ‑value 0.10<?<0.15

?<0.0005

?>0.0005

0.0005<?<0.001

Is there evidence that microwaving significantly increases the pressure needed to break a cracker?

There is significant evidence microwaving increases the pressure needed to break a cracker.

There is little evidence microwaving increases the pressure needed to break a cracker.

There is significant evidence microwaving decreases the pressure needed to break a cracker.

None of the options is correct.

To examine how large is the increase in the mean pressure needed to break a cracker, a 95% confidence interval, using the conservative degrees of freedom, for the difference in means ?1−?2 is

62.6±18.95 .

60.6±5.793 .

52.6±15.760 .

77.2±20.905 .

CONCLUDE: What does the confidence interval indicate?

We are 95% confident that microwaving crackers increases their mean breaking strength by between 43.65 and 81.55 psi.

Microwaving crackers increases their mean breaking strength approximately 95% of the time.

There is a 95% chance that microwaving crackers increases their mean breaking strength by between 43.65 and 81.55 psi.

We are 95% confident that microwaving crackers increases their mean breaking strength by between 54.807 and 66.393 psi.

Answer 1

a)

b) We will be using

two samples, inference about mean

P value<0.0005

There is significant evidence microwaving increases the pressure needed to break a cracker.

c)

62.6±18.95 .

We are 95% confident that microwaving crackers increases their mean breaking strength by between 43.65 and 81.55 psi.