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M650

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Statistics

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Jan 9, 2024

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docx

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M650 Question 1 Match up the following:  Doesn't have a match - 7  Increasing significance level α - 1  "H0: Mean ≥ value" is rejected if: - 4  A one-sided test with lower reject region does not reject H0 if: - 6  "H0: Mean ≤ value" is rejected if: - 3  "H0: Mean = value" is rejected if: - 2  A one-sided test with upper reject region does not reject H0 if : - 5 ------------------------------------------------------ 1. Increases the chance of a type I error and decreases the chance of a type 2 error 2. If either test statistic < negative critical value, or test statistic > positive critical value 3. Test statistic > positive critical value 4. Test statistic < negative critical value 5. Test statistic < positive critical value 6. Test statistic > negative critical value 7. Decreases the chance of a type I and increases the chance of a type II error Question 2 Match up the following:  Reduce the chance of a type 1 error. - 3  Statistically significant differences do not necessarily require rejecting the status quo. - 5  Not rejecting H0 does not prove H0. - 2  Always take action if H0 is rejected. - 6  Reduce the chance of a type 2 error. - 4  Rejecting H0 does not prove HA. - 1 ------------------------------------------------------ 1. A type 1 error is possible. 2. A type 2 error is possible. 3. Decrease the significance level. 4. Increase sample size.

M650 5. Small differences without sufficient benefit can be made statistically significant by increasing sample size. 6. False Question 3 Match up the following:  You want to decide if a sample matches a multinomial probability distribution with P(event A) = 0.15, P(Event B) = 0.25, P(Event C) = 0.35, and P(Event D) = 0.25. - 8  Crop yield was measured on multiple acreages with different fertilizer treatments. You want to know if the yields are equal . - 6  A simple random sample of beer drinkers are categorized and counted by gender and by beer preferences light, regular, or dark beer. Is there a relationship between counts and categories? - 9  Decide if time (min) spent on a new web site before customers make a purchase is less than the time on old web site of 2 minutes. - 2  Last year, 2 employees enrolled in a wellness class. From a random sample taken this year, decide if more are planning to take a wellness class. - 3  Marketing wants to know if applications by Silver, Gold, or Platinum credit card are the same for the past three mailings. Applications are counted by type of card and mailing. - 7  Last year, on average, 2 accounting reports/quarter were late. From a random sample taken this year, decide if the number of late reports has changed. - 1 ------------------------------------------------------ 1. H0: Mean = 2 2. H0: Mean ≥ 2 3. H0: Mean ≤ 2 4. H0: Mean ≠ 2 5. H0: Mean > 2 6. H0: Means equal 7. H0: Homogeneous 8. H0: Good fit 9. H0: Independence Question 4

M650 Match up the following ANOVA statements:  Pieces of white cloth were coated with the same amount of a grease. Washed with hot or cold water, and with short or long wash times, cleanness was measured. What type of analysis is required? - 4  An Internet site randomly sent customers to one of three versions of its site and recorded how long each user stayed on a site. What kind of analysis is required? - 3  The test statistic F rejects H0. - 8  To test a new laundry detergent, pieces of white cloth were coated with the same amount of a grease. After hot or cold water, combined with short or long wash times, cleanness was measured. What are the factors? - 1  The test statistic moves in the direction of HA and pvalue decreases. - 7  The spread within samples decreases and the spread between sample means increases. - 5  The spread within samples increases and the spread between sample means decreases. - 6  Mrs. Fields food lab evaluated chocolate chips for their chocolate chip cookies. They baked cookies with different kinds of chips (milk, dark, and semi-sweet chocolate). Expert cookie testers ranked the cookies on a 5-point Likert scale. What are the levels of the factor? - 2  In ANOVA, H0 is rejected means that - 9 ------------------------------------------------------ 1. Water temperature and washing time 2. milk, dark, and semi-sweet 3. 1-way ANOVA 4. 2-way ANOVA 5. The F test statistic increases. 6. The F test statistic decreases. 7. True 8. The test statistic is greater than the critical value. 9. The means are not all equal. 10. False 11. Chi Square test Question 5

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M650 Five different paints are marketed as having the same drying time. To verify the manufacturer's claim, the dry times of paints were measured in seconds and recorded in DATA (Click and download). Test the claim that the drying times are equal at α = 0.05.  The F test statistic 0.535 does not exceed the critical value 2.579 and indicates that the data provide insignificant evidence against H0. H0 is not rejected at α = 0.05.  The F test statistic 1.338 does not exceed the critical value 2.579 and indicates that the data provide insignificant evidence against H0. H0 is not rejected at α = 0.05.  The F test statistic 123.4 exceeds the critical value 2.579 and indicates that the data provide significant evidence against H0. H0 is rejected at α = 0.05. Action is required.  None of the answers match my ANOVA.  The pvalue of 4.2E-22 indicates that the data provide significant evidence against H0. H0 is rejected at α = 0.05. Action is required.  The pvalue of 3.73E-20 indicates that the data provide significant evidence against H0. H0 is rejected at α = 0.05. Action is required. Question 6 Auditors make assessments on the bases of their individual experience, the experience of others, or a combination of experiences. A study of the auditors' methods was performed. The average number of errors is recorded in DATA (Click and download). At α = 0.10, test the claim that errors are equal.  The pvalue of 0.0998 is less than alpha = 0.10 and rejects H0. The audit methods are not equal.  The F test statistic of 5.151 exceeds the critical value 2.406 and rejects H0 at alpha = 0.10. The audit methods are not equal.  The pvalue of 0.353 is greater than alpha = 0.10 and does not reject H0. It remains plausible that the audit methods are equal.  The F test statistic of 0.208 is less than the critical value 2.406 and does not reject H0 at alpha = 0.10. It remains plausible that the audit methods are equal.  None of the answers are correct.  The pvalue of 0.402 is greater than alpha = 0.10 and does not reject H0. It remains plausible that the audit methods are equal. Question 7 Match up the following Chi Square statements:  Tests if specified distribution of H0 matches a sample - 1  Tests if category labels in a 2-way classification table have some meaningful relationship to counts - 2  test statistic increases - 6

M650  Tests if multiple unspecified probability distributions are the same - 3  = X - 1 - number of estimated distribution parameters - 5  test statistic > critical value - 8  = (X-1)(Y-1) - 4  p value increases - 7 ------------------------------------------------------ 1. Goodness of fit 2. Independence 3. Homogeneity 4. It is the DF for a two-way contingency table of X rows and Y columns. 5. It is the DF for a goodness of fit with X cells, a one-way table. 6. The difference between observed and expected counts increases. 7. The test statistic decreases. 8. H0 is rejected. Question 8 The Director of Human Resources at a large company wants to determine if there are any irregularities in the use of employee sick leave. The number of employees on sick leave was recorded each day for a 6 months and subtotaled by day. Open DATA (← Click and Open). At significance level 0.05, test H0: Daily sick leave useage is consistent (equal).  The pvalue 0.20 > α is not significant evidence against H0, and does not reject H0. The sick leave policies and procedures are working.  None of the answers match my chi square results.  The chi square statistic 11.15 exceeds the critical value 9.49 and rejects H0. Action is required to characterize the inconsistency and revise policy as needed.  The pvalue 0.44 > α is not significant evidence against H0, and does not reject H0. The sick leave policies and procedures are working.  The chi square statistic 17.1 exceeds the critical value 9.49 and rejects H0. Action is required to characterize the inconsistency and revise policy as needed.  The chi square statistic 20 exceeds the critical value 9.49 and rejects H0. Action is required to characterize the inconsistency and revise policy as needed. Question 9

M650 Often frequency data are tabulated according to two categories to decide if there is a relationship between categories and counts, in other words. Do the categories matter? Machine shop Hi Tech errors are tabulated by Shift and Machine with significance level α in DATA (Click and Open). Are the machines and shifts operating consistently? Perform the appropriate test.  The chi square statistic 24.375 does not exceed the critical value 29.14 and fails to reject H0.  The chi square statistic 17.554 does not exceeds the critical value 21.06 and fails to reject H0.  The pvalue 0.074 < α is significant evidence against H0, rejects H0, and action is needed to improve machine errors.  The pvalue 0.018 < α is significant evidence against H0, rejects H0, and action is needed to improve machine errors.  The chi square statistic 3.085 does not exceeds the critical value 23.68 and fails to reject H0.  None of the answers match my chi square results. Question 10 Candy colors in boxes were counted by company (A, B, and C). Test H0: Distribution of colors is the same using alpha and counts in DATA (Click and Open) ALPHA 0.001 Candy Company A B C Brown 16 21 55 Yellow 139 128 247 Red 327 349 184 Orange 322 338 202 Green 136 151 247 Blue 25 29 43  The pvalue 0.01 < standard significance level. The evidence against H0 is strong. H0: "Distributions of colors are the same" is rejected.  The chi square statistic 5.8 does not exceeds the critical value of 15.99. pvalue 0.83. H0 is not rejected at α = 0.10 (sensitive, exploratory). Keep the status quo, or it is plausible that the distributions of colors are the same.  The chi square statistic 5.54 does not exceeds the critical value of 23.21. H0 is not rejected. Keep the status quo, or it is plausible that the distributions of colors are the same.  The pvalue 0.90 > alpha 0.05. H0 is not rejected. Keep the status quo, or it is plausible that the distributions of colors are the same.  None of the answers match my chi square results.

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