Problem Scenario 1:
Following is a problem description. Use the mean & variance provided to answer the questions which follow, showing all calculations BY HAND. For all hypothesis tests, you MUST show all 7 steps we have been using and use the CRITICAL VALUE METHOD to make your decision. Treat each question as a separate problem — we use the same data set, but are answering different research questions.
Irradiation of Food
The irradiation of food to destroy bacteria is a growing phenomenon. In order to determine which one of two methods of irradiation is best, a scientist took a random sample of 100 one- pound packages of minced meat and subjected 50 of them to irradiation Method 1 and the remaining 50 to irradiation Method 2. The bacteria count was measured and the following statistics were computed. The scientist noted that the
data are normally distributed.
NOTE: use ONLY the Critical Value method for hypothesis tests. If you include both rules in step 4 or include both in your decision step, I will have to conclude that you do not yet understand them.
Method 1
x1 86
s12 324

Method 2
x 2 98
2
s 2 841

2

a.) Estimate with 95% confidence the mean bacteria count with Method 2. Interpret the interval.

3

b.) An important factor in determining which method to choose is consistency. That is, all other things being equal wed prefer to have a method that leaves all irradiated food with approximately the same bacteria count. Can we infer at the 5% significance level that Method 1 is superior to Method 2 in this respect?

4

c.) Estimate with 95% confidence the difference in the mean bacteria count between Method 1 and Method 2. Interpret the interval.

5

d.) Can we conclude at the 5% significance level that the variance of the bacteria count with Method 2 is less than 1,500?

6

Problem Scenario 2:
Following is a problem description. For all hypothesis tests, you MUST show all 7 steps we have been using and use the P-VALUE METHOD to make your decision. For confidence intervals, there are not specific steps, but there is a specific Excel tool for each interval. They should not be done by-hand for this set, nor should you simply use Excel formulas to use it as a calculator. Treat each question as a separate problem -we use the same data set, but are answering different research questions.
Many parts of cars are mechanically tested to be certain that they do not fail prematurely. In an experiment to determine which one of two types of metal alloy produces superior door hinges, 40 of each type were tested until they failed. Car manufacturers consider any hinge that does not survive 1 million openings and closings to be a failure. The number of openings and closings as observed and recorded in the
accompanying table (to the closest .1 million). A statistician has determined that the number of openings and closings is normally distributed.
NOTE: use ONLY the P-value method for hypothesis tests. If you include both rules in step 4 or include both in your decision step, I will have to conclude that you do not yet understand the p-value rule.

1.5
1.8
1.6
1.3
1.2
1.1
1.3
1.1
0.9
1.1

Number of Openings and Closings
Alloy 1
Alloy 2
1.5
0.9
1.3
1.4
0.9
1.3
1.6
1.3
1.5
1.3
1.3
0.9
1.2
1.2
1.8
0.7
1.2
1.1
0.9
1.5
1.6
1.2
0.8
1.2
1.3
1.4
1.4
0.8
0.7
1.1
1.5
1.1
1.5
1.1
1.4
0.8
0.8
0.8
1.1
1.3
1.1
1.5
1.6
1.6
1.3
1.4
1.2
1.3
1.4
1.7
0.9
0.6
0.9
1.8
1.3
1.9
1.3
1.5
0.8
1.6

0.8
1.4
0.9
1.1
1.4
0.8
0.9
1.6
1.4
1.3

7

a) Can we conclude at the 5% significance level that the mean number of door openings and closings with hinges made from Alloy 1 is greater than 1.25 million?

8

b.) Estimate with 90% confidence the variance of the number of openings and closings with the hinges made from Alloy 2. Interpret the interval.

9

c.) Do the data provide enough evidence to allow us to infer at the 5% significance level that hinges made with Alloy1 last longer than hinges made with Alloy 2?

10

d.) The quality control manager is not only concerned about the openings and closings of the hinges, but is also concerned about the proportion of hinges that fail. Can we infer at the 10% significance level that the proportion of hinges made with Alloy 2 that fail exceeds 18%?

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