NOTE: Since this question asks about the relationship between to population vari
ID: 3126231 • Letter: N
Question
NOTE: Since this question asks about the relationship between to population variances, the F-Test for Two Variances tool will be used. View the data table & copy the data into Excel. Use Excel's F-Test for Two Variances tool to complete the required calculations to answer this question.
Tests of product quality by human inspectors can lead to serious errors. To evaluate the performance of inspectors in a new company, a quality manager had a sample of 12 novice inspectors evaluate 200 finished products. The same 200 items were evaluated by 12 experienced inspectors. The quality of each item, defective or non-defective, was known to the manager. The accompanying table lists the number of inspection errors (classifying a defective item as non-defective or vice versa) made by each inspector. Complete parts A & B below.
A. Prior to conducting this experiment, the manager believed that the variance in inspection errors was lower for experienced inspectors than for novice inspectors. Does the sample data support her belief? Test using ? = 0.05
Set up the null & alternative hypotheses for testing this assumption. (Treat the novice inspectors as population 1)
Please select either A. > B. < C. = or D. ? for both the null & alternative.
Ho: ? 2 ___ ? 2
1 2
Ha: ? 2 ___ ? 2
1 2
Compute the test statistic: The test statistic is F = _____ (Round to three decimal places as needed)
Find the rejection region for the test using ? = 0.05
The rejection region is F > ______ (Round two decimal places as needed)
Interpret the result. Choose correct answer below
1. Since the test statistic does not fall in the rejection region, do not reject Ho. There is INSUFFICIENT evidence to support the manager’s belief.
2. Since the test statistic does not fall in the rejection region, do not reject Ho. There is SUFFICIENT evidence to support the manager’s belief.
3. Since the test statistic does not fall in the rejection region, reject Ho. There is SUFFICIENT evidence to support the manager’s belief.
4. Since the test statistic does not fall in the rejection region, reject Ho. There is INSUFFICIENT evidence to support the manager’s belief.
B. What is the appropriate p-value of the test you conducted in part A?
p-value = ____ (round to three decimal places as needed)
Inspection Errors Full data set ovice Inspectors Experienced Inspectors 32 35 34 35 20 29 26 40 45 32 21 49 32 28 17 19 18 25 1 20 21 14 25 18
Explanation / Answer
NOTE: Since this question asks about the relationship between to population variances, the F-Test for Two Variances tool will be used. View the data table & copy the data into Excel. Use Excel's F-Test for Two Variances tool to complete the required calculations to answer this question.
Tests of product quality by human inspectors can lead to serious errors. To evaluate the performance of inspectors in a new company, a quality manager had a sample of 12 novice inspectors evaluate 200 finished products. The same 200 items were evaluated by 12 experienced inspectors. The quality of each item, defective or non-defective, was known to the manager. The accompanying table lists the number of inspection errors (classifying a defective item as non-defective or vice versa) made by each inspector. Complete parts A & B below.
A. Prior to conducting this experiment, the manager believed that the variance in inspection errors was lower for experienced inspectors than for novice inspectors. Does the sample data support her belief? Test using = 0.05
Set up the null & alternative hypotheses for testing this assumption. (Treat the novice inspectors as population 1)
Please select either A. > B. < C. = or D. for both the null & alternative.
Ho: 2 = 2
1 2
Ha: 2 > 2
1 2
Compute the test statistic: The test statistic is F = 2.155 (Round to three decimal places as needed)
Find the rejection region for the test using = 0.05
The rejection region is F > 2.82 (Round two decimal places as needed)
Interpret the result. Choose correct answer below
1. Since the test statistic does not fall in the rejection region, do not reject Ho. There is INSUFFICIENT evidence to support the manager’s belief.
2. Since the test statistic does not fall in the rejection region, do not reject Ho. There is SUFFICIENT evidence to support the manager’s belief.
3. Since the test statistic does not fall in the rejection region, reject Ho. There is SUFFICIENT evidence to support the manager’s belief.
4. Since the test statistic does not fall in the rejection region, reject Ho. There is INSUFFICIENT evidence to support the manager’s belief.
B. What is the appropriate p-value of the test you conducted in part A?
p-value =0.109 (round to three decimal places as needed)
F Test for Differences in Two Variances
Data
Level of Significance
0.05
Larger-Variance Sample
Sample Size
12
Sample Variance
76.1515
Smaller-Variance Sample
Sample Size
12
Sample Variance
35.3333
Intermediate Calculations
F Test Statistic
2.1552
Population 1 Sample Degrees of Freedom
11
Population 2 Sample Degrees of Freedom
11
Upper-Tail Test
Upper Critical Value
2.8179
p-Value
0.1093
Do not reject the null hypothesis
F Test for Differences in Two Variances
Data
Level of Significance
0.05
Larger-Variance Sample
Sample Size
12
Sample Variance
76.1515
Smaller-Variance Sample
Sample Size
12
Sample Variance
35.3333
Intermediate Calculations
F Test Statistic
2.1552
Population 1 Sample Degrees of Freedom
11
Population 2 Sample Degrees of Freedom
11
Upper-Tail Test
Upper Critical Value
2.8179
p-Value
0.1093
Do not reject the null hypothesis
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