A survey of 35 museums asked to provide the performance measure used most often for intermal evaluation A summary of the results is provided in the table. The data were analyzed using a chi-square test for a multinomial experiment. The results are shown in the accompanying table Complete parts and b Click the icon to view the results a. Is there evidence to indicate that one performance measure is used more often than any of the others? Test using a 0.1 Determine the null and atemative hypotheses for testing whether one performance measure is used more often than any of the other types. Choose the correct answer below OA M₂ Pj "P₂ P₂P "Pg -0.20 H₂: Py *P₂ *Dy *P *Ps OB M₂ D₂ D₂**P₂ At least one of the mutinomial probabilities equals its hypothesized value -OC. M₂ P P₂ P₂P P₂020 H, At least one of the multinomial probabilities does not equal its hypothesized value OD H₂ At least one of the multinomial probabilities differs from its hypothesized value M₂ Pj "P₂ P₂ P₂ -0.20 identify the best statistic 2 Round to three decimal places as needed) dentify the pal Round to three decimal places as needed) Choose the corect conclusion below OA Reject H, There is insufficient evidence that at least one performance measure is used more often than any of the other types OC. Fail to reject M₂. There is insufficient evidence that at least one performance measure is used more often than any of the other types Find a 90% confidence internal for the proportion of museums worldwide that use total visitors as their performance measure Interpret the result Select the correct choice below and it in the answer boxes to complete your choice Round to three decimal places as needed) OA There is 90% confidence that the true proportion of museums that use total visitors as their performance measure is between OB. Reject H. There is sufficient evidence that at least one performance measure is used more often than any of the other types OD Fail to reject M₂. There is sufficient evidence that at least one performance measure is used more often than any of the other types

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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4.
A survey of 35 museums asked to provide the performance measure used most often for internal evaluation. A summary of the results is provided in the table. The data were analyzed using a chi-square test for a multinomial experiment. The results are shown in the accompanying table. Complete parts a and b.
Click the icon to view the results.
a. Is there evidence to indicate that one performance measure is used more often than any of the others? Test using a 0.1.
Determine the null and alternative hypotheses for testing whether one performance measure is used more often than any of the other types. Choose the correct answer below.
O A. Ho: P₁
P₂ = P3 P4 P5 = 0.20
Ha: P₁
P₂ P3 P4 P5
O B. Ho: P₁
P₂ # P3
P4 P5
H₁: At least one of the multinomial probabilities equals its hypothesized value.
O C. Ho: P₁ P₂ = P3
P4 P5 = 0.20
Ha: At least one of the multinomial probabilities does not equal its hypothesized value.
O D. Ho: At least one of the multinomial probabilities differs from its hypothesized value.
Ha: P₁ P₂ = P3 P4 P5 = 0.20
Identify the test statistic.
x² =
(Round to three decimal places as needed.)
Identify the p-value.
(Round to three decimal places as needed.)
Choose the correct conclusion below.
O A. Reject Ho. There is insufficient evidence that at least one performance measure is used more often than any of the other types.
O C. Fail to reject Ho. There is insufficient evidence that at least one performance measure is used more often than any of the other types.
b. Find a 90% confidence interval for the proportion of museums worldwide that use total visitors as their performance measure. Interpret the result.
Select the correct choice below and fill in the answer boxes to complete your choice.
(Round to three decimal places as needed.)
and
O A. There is 90% confidence that the true proportion of museums that use total visitors as their performance measure is between
OB. The proportion of museums that respond with total visitors as their performance measure is between
and
OC. The proportion of samples that have 90% of museums using total visitors as their performance measure is between
and
1: Chi-square test for a multinomial experiment results
Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: NUMBER
Using category names in PERFORM
Category
Observed
Total visitors
9
Paying visitors
3
Big shows
7
Funds raised
5
Members
11
DF
Chi-Sq
4
5.714286
N
35
Test Proportion
0.2
0.2
0.2
0.2
0.2
P-value
0.222
OB. Reject Ho. There is sufficient evidence that at least one performance measure is used more often than any of the other types.
O D. Fail to reject Ho. There is sufficient evidence that at least one performance measure is used more often than any of the other types.
Expected
7
Contribution to Chi-SQ
0.571429
2.285714
0.000000
0.571429
2.285714
7
7
7
7
Performance
Measure
Total visitors
Paying visitors
Big shows
Funds raised
Members
Number of
Museums
X
3
7
5
11
Transcribed Image Text:4. A survey of 35 museums asked to provide the performance measure used most often for internal evaluation. A summary of the results is provided in the table. The data were analyzed using a chi-square test for a multinomial experiment. The results are shown in the accompanying table. Complete parts a and b. Click the icon to view the results. a. Is there evidence to indicate that one performance measure is used more often than any of the others? Test using a 0.1. Determine the null and alternative hypotheses for testing whether one performance measure is used more often than any of the other types. Choose the correct answer below. O A. Ho: P₁ P₂ = P3 P4 P5 = 0.20 Ha: P₁ P₂ P3 P4 P5 O B. Ho: P₁ P₂ # P3 P4 P5 H₁: At least one of the multinomial probabilities equals its hypothesized value. O C. Ho: P₁ P₂ = P3 P4 P5 = 0.20 Ha: At least one of the multinomial probabilities does not equal its hypothesized value. O D. Ho: At least one of the multinomial probabilities differs from its hypothesized value. Ha: P₁ P₂ = P3 P4 P5 = 0.20 Identify the test statistic. x² = (Round to three decimal places as needed.) Identify the p-value. (Round to three decimal places as needed.) Choose the correct conclusion below. O A. Reject Ho. There is insufficient evidence that at least one performance measure is used more often than any of the other types. O C. Fail to reject Ho. There is insufficient evidence that at least one performance measure is used more often than any of the other types. b. Find a 90% confidence interval for the proportion of museums worldwide that use total visitors as their performance measure. Interpret the result. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to three decimal places as needed.) and O A. There is 90% confidence that the true proportion of museums that use total visitors as their performance measure is between OB. The proportion of museums that respond with total visitors as their performance measure is between and OC. The proportion of samples that have 90% of museums using total visitors as their performance measure is between and 1: Chi-square test for a multinomial experiment results Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: NUMBER Using category names in PERFORM Category Observed Total visitors 9 Paying visitors 3 Big shows 7 Funds raised 5 Members 11 DF Chi-Sq 4 5.714286 N 35 Test Proportion 0.2 0.2 0.2 0.2 0.2 P-value 0.222 OB. Reject Ho. There is sufficient evidence that at least one performance measure is used more often than any of the other types. O D. Fail to reject Ho. There is sufficient evidence that at least one performance measure is used more often than any of the other types. Expected 7 Contribution to Chi-SQ 0.571429 2.285714 0.000000 0.571429 2.285714 7 7 7 7 Performance Measure Total visitors Paying visitors Big shows Funds raised Members Number of Museums X 3 7 5 11
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