1. A manufacturing company produces part 2205 for the aerospace industry. This particular part can be manufactured using 3 different production processes. The management wants to know if the quality of the units of part 2205 is the same for all three processes. The producion supervisor obtained the following data: The Process 1 had 29 defective units in 240 items; Process 2 produced 12 defective units in 180 items and Process 3 manufactured 9 defective units in 150 items.

Chi-square Contingency Table Test for Independence

                                    Col 1           Col 2           Col 3           Total

    Row 1 Observed    29                12                9                  50

               Expected     21.05           15.79           13.16           50.00

               (O - E)² / E 3.00             0.91             1.31             5.22

    Row 2 Observed    211              168              141              520

               Expected     218.95         164.21         136.84         520.00

               (O - E)² / E 0.29             0.09             0.13             0.50

    Total   Observed    240              180              150              570

               Expected     240.00         180.00         150.00         570.00

               (O - E)² / E 3.29             1.00             1.44             5.73



                                    5.73             chi-square

                                    .0571           p-value

At a significance level of .05, the management wants to perform a hypothesis test to determine if the quality of the items produced appears to be independent of the production process used. Based on the results summarized in the output provided in the table above, we:

Reject H0 and conclude that the quality of the product is not the same for all processes.

Reject H0 and conclude that the quality of the product is dependent on the manufacturing process.

Fail to reject H0 and conclude that the quality of the product does not significantly differ among the three processes.

Fail to reject H0 and conclude that the quality of the product is not the same for all processes.

Reject H0 and conclude that the quality of the product is independent of the manufacturing process used.

2. A real estate company is analyzing the selling prices of residential homes in a given community. 140 homes that have been solved in the past month are randomly selected and their selling prices are recorded. The statistician working on the project has stated that in order to perform various statistical tests, the data must be distributed according to normal distribution. In order to determine whether the selling prices of homes included in the random sample are normally distributed, the data is divided into 6 classes of equal size and the number of observations in each class is recorded. The chi-square goodness of fit test for normal distribution is performed and the results are summarized in the following table:

Goodness of Fit Test

     Observed     expected      O - E             (O - E)² / E    % of chisq

    10                  3.192             6.808             14.520           64.81

    23                  19.026           3.974             0.830             3.70

    37                  47.782           -10.782          2.433             10.86

    40                  47.782           -7.782            1.267             5.66

    27                  19.026           7.974             3.342             14.92

    3                    3.192             -0.192            0.012             0.05

    140                140.000         0.000             22.404           100.00



            22.40   Chi-square

            .0001   p-value

What is the appropriate null hypothesis?

H0: The residential home selling prices are distributed according to normal distribution.

H0: The residential home selling prices are not distributed according to normal distribution.

H0: The distribution of residential home selling prices is either right or left skewed.

H0: The distribution of the residential home selling prices is symmetric.

None of the above is correct.

Name: 1. A manufacturing company produces part 2205 for the aerospace indust
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: 1. A manufacturing company produces part 2205 for the aerospace industry. This particular part can be manufactured using 3 different production processes. The management wants to know if the quality of the units of part 2205 is the same for all three

Question

1. A manufacturing company produces part 2205 for the aerospace industry. This particular part can be manufactured using 3 different production processes. The management wants to know if the quality of the units of part 2205 is the same for all three processes. The producion supervisor obtained the following data: The Process 1 had 29 defective units in 240 items; Process 2 produced 12 defective units in 180 items and Process 3 manufactured 9 defective units in 150 items.

Chi-square Contingency Table Test for Independence

Col 1 Col 2 Col 3 Total

Row 1 Observed 29 12 9 50

Expected 21.05 15.79 13.16 50.00

(O - E)² / E 3.00 0.91 1.31 5.22

Row 2 Observed 211 168 141 520

Expected 218.95 164.21 136.84 520.00

(O - E)² / E 0.29 0.09 0.13 0.50

Total Observed 240 180 150 570

Expected 240.00 180.00 150.00 570.00

(O - E)² / E 3.29 1.00 1.44 5.73

5.73 chi-square

.0571 p-value

At a significance level of .05, the management wants to perform a hypothesis test to determine if the quality of the items produced appears to be independent of the production process used. Based on the results summarized in the output provided in the table above, we:

		Reject H0 and conclude that the quality of the product is not the same for all processes.
		Reject H0 and conclude that the quality of the product is dependent on the manufacturing process.
		Fail to reject H0 and conclude that the quality of the product does not significantly differ among the three processes.
		Fail to reject H0 and conclude that the quality of the product is not the same for all processes.
		Reject H0 and conclude that the quality of the product is independent of the manufacturing process used.

2. A real estate company is analyzing the selling prices of residential homes in a given community. 140 homes that have been solved in the past month are randomly selected and their selling prices are recorded. The statistician working on the project has stated that in order to perform various statistical tests, the data must be distributed according to normal distribution. In order to determine whether the selling prices of homes included in the random sample are normally distributed, the data is divided into 6 classes of equal size and the number of observations in each class is recorded. The chi-square goodness of fit test for normal distribution is performed and the results are summarized in the following table:

Goodness of Fit Test

Observed expected O - E (O - E)² / E % of chisq

10 3.192 6.808 14.520 64.81

23 19.026 3.974 0.830 3.70

37 47.782 -10.782 2.433 10.86

40 47.782 -7.782 1.267 5.66

27 19.026 7.974 3.342 14.92

3 3.192 -0.192 0.012 0.05

140 140.000 0.000 22.404 100.00

22.40 Chi-square

.0001 p-value

What is the appropriate null hypothesis?

		H0: The residential home selling prices are distributed according to normal distribution.
		H0: The residential home selling prices are not distributed according to normal distribution.
		H0: The distribution of residential home selling prices is either right or left skewed.
		H0: The distribution of the residential home selling prices is symmetric.
		None of the above is correct.

Accepted Answer

Answered: Image /qna-images/answer/43ac7c80-eee8-4979-86a7-6af314acbba8.jpg