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 p1−p2 is:______a. 0.806±0.083 .b. 0.831±0.079 .c. 0.756±0.124d. 0.806±0.099 .

Answer 1

1. Yes

2. 83%

Explanation:

Does microwaving significantly improve indicators of future breaking?

Yes, this is because the normal requirements based on the 95% confidence implies having a deviation of only 5%. That is, it should fall within 5% of 65 newly baked crackers =5% x 65= 3.25. Thus, since only 3 of the 65 microwaved crackers showed visible cracking we could be confident.

How large is the improvement? What do you conclude about the idea of microwaving crackers?

Approximately there was an 83.08% (57/65 *100 - 3/65 *100) improvement.

The conclusion is that there is a statistically significant relationship between microwaving and reducing cracking.