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Name: Ch. 13 Review 1. A chi-square goodness of fit test is used to test whether a 0 to9 spinner is “fair” (that is, the outcomes are all equally likely). The spinner is spun 100 times, and the results are recorded. Which member of the chi-square family of curves is used? 2 2 2 2 (a) (8) (b) (9) (c) (10) (d) (99) (e) None of the above 2. A study of accident records at a large engineering company in England reported the following number of injuries on each shift for 1 year: Shift: Number of injuries: Morning 1372 Afternoon 1578 Night 1686 Is there sufficient evidence to say that the numbers of accidents on the three shifts are not the same? Test at the 0.05, 0.01, and 0.001 levels. (a) There is sufficient evidence at all three levels to say that the numbers of accidents on each shift are not the same. (b) There is sufficient evidence at the 0.05 and 0.01 levels but not at the 0.001 level. (c) There is sufficient evidence at the 0.05 level but not at the 0.01 or 0.001 levels. (d) There is sufficient evidence at the 0.001 level but not at the 0.01 or 0.05 levels. (e) There is insufficient evidence at any of these levels. Questions 3 to 10 refer to the following situation. In the paper “Color Association of Male and Female Fourth-Grade School Children” (Journal of Psychology, 1988, 383–388), reported on a study in which children were asked to indicate what emotion they associated with the color red. The response and the sex of the child are noted and summarized below. The first number in each cell is the count; the second number is the row percent. Female Male Total Statistic Pearson Chi-Square Likelihood Ratio Chi-Square Mantel-Haenszel Chi-Square Anger 27 26.47 34 30.36 61 Happy 19 18.63 12 10.71 31 DF * * 1 Love 39 38.24 38 33.93 77 Pain 17 16.67 28 25.00 45 Value 4.629 4.661 0.307 Total 102 112 214 Prob ***** ***** ***** 3. The null hypothesis is (a) emotional association with red is independent of gender. (b) gender is dependent upon the emotional association with red. (c) the probability of associating a specific emotion with red is related to gender. (d) the number of children in each cell does not depend upon gender or upon emotion. (e) the color red is independent of the emotion associated with it and with gender. 4. Under a suitable null hypothesis, the expected frequency for the cell corresponding to Anger and Males is (a) 15.9. Chapter 13 1 14AB (b) 55.7. (c) 30.4. (d) 31.9. (e) 29.1. 5. The null hypothesis will be rejected at = 0.05 if the test statistic exceeds (a) 3.84. (b) 5.99. (c) 7.81. (d) 9.49. (e) 14.07. 6. The approximate P-value is (a) between 0.100 and 0.900. (b) between 0.050 and 0.100. (c) between 0.025 and 0.050. (d) between 0.010 and 0.025. (e) between 0.005 and 0.010. 7. Which of the following is NOT CORRECT? (a) The children were classified by sex and emotion associated with red. Each child was counted in one and only one cell. (b) The null hypothesis is that the type of emotion associated with red is independent of the sex of the child. (c) The null hypothesis is that the proportion of emotions associated with red is the same for both sexes. (d) All expected cell counts should be greater than 5 in order that the distribution of the test statistic is an approximate chi-square distribution. (e) If we reject the null hypothesis, then we have proven that the two sexes associate red with emotions in different ways. 8. Which of the following is NOT CORRECT? (a) A lower percent of female students associate the emotion “anger” with the color red than do male students. (b) More students associate the color red with the emotion “love” than with the emotion “anger.” (c) There is insufficient evidence of an association between gender and emotion associated with the color red. (d) We will be unable to compute a correlation for these data because the variables are both categorical. (e) We compute row or column percents by dividing the cell count by the table total (214). 9. A Type I error would be committed if (a) we conclude that the sex of the child and the emotion associated with red are independent when in fact they are not independent. (b) we conclude that the sex of the child and the emotion associated with red are not independent when in fact they are not independent. (c) we conclude that the proportion of emotions associated with red differs between males and females when in fact they are the same. Chapter 13 2 14AB (d) we conclude that the proportion of emotions associated with red is the same for males and females when in fact they are the same. (e) we fail to find any association between the color red and emotions for either sex. 10. The test statistic and approximate P-value are (a) 4.661 0.1983 (b) 4.661 0.3966 (c) 4.629 0.2011 (d) 4.629 0.4022 (e) 4.629 0.1006 Questions 11 to 13 relate to the following situation. A sample of 102 drug users was interviewed and each subject was asked to name the kind of drug that each first injected. Here are the results: First drug injected Heroin Speed Other Number 42 36 24 11. An appropriate null hypothesis is (a) the count of first drug injected is the same for each drug category. (b) µ = 34. (c) at least one of the cell counts is different from the other two. (d) the proportion of first drug injected depends on the type of drug. (e) the 3 cell counts are independent of the type of drug. 12. The test statistic, degrees of freedom, and P-value are (a) 4.94, 2, 0.0845. (b) 1.88, 2, 0.391. (c) 2.94, 3, 0.40. (d) 0.118, 2, 0.94. (e) 8.94, 2, 0.011. 13. Which of the following is a correct statement? In order to make an inference about the population, (a) the population has to be at least 10 times the size of the sample. (b) the cell counts for our sample have to be approximately the same as the counts for the host population. (c) all observed cell counts have to be positive, and no more than 20% can be less than 15. (d) the sample has to have the same characteristics as the population. (e) the subjects have to be a random sample of drug users. 14. Are all employees equally prone to having accidents? To investigate this hypothesis, a researcher looked at a light manufacturing plant and classified the accidents by type and by age of the employee. Age Under 25 25 or over Sprain | 9 | 61 Accident Type Burn 17 13 Cut 5 12 A chi-square test gave a test statistic of 20.78. If we test at = 0.05 Chapter 13 3 14AB (a) there appears to be no association between accident type and age. (b) age seems to be independent of accident type. (c) accident type does not seem to be independent of age. (d) there appears to be a 20.78% correlation between accident type and age. (e) the proportion of sprain, cuts, and burns seems to be similar for both age classes. 15. Each person in a random sample of 50 was asked to state his/her sex and preferred color. The resulting frequencies are shown below. Male Female Red 5 15 Color Blue Green 14 6 6 4 A chi-square test is used to test the null hypothesis that sex and preferred color are independent. Which of the following statements is a correct decision about the null hypothesis? (a) Reject at the 0.005 level. (b) Reject at the 0.01 level but not at the 0.005 level. (c) Reject at the 0.025 level but not at the 0.01 level. (d) Reject at the 0.05 level but not at the 0.025 level. (e) Accept at the 0.05 level. 16. The following data were obtained from a company that manufactures special plastic containers that are to hold a specified volume of hazardous material. On each of the three 8-hour shifts workers are able to make 500 of the containers. Some containers do not meet specifications as required by the company’s customer because they are too small; others, because they are too large. Shift 8 am 4 pm Midnight Too small 36 24 12 Conformance to Specification Within spec. Too large 452 12 443 33 438 50 If conformance to specifications is independent of shift, the expected number of containers that meet specifications on the 4 pm shift is (a) 166.7. (b) 443. (c) 33. (d) 444.3. (e) 500. 17. A survey was conducted to investigate whether alcohol consumption and smoking are related. The following information was compiled for 600 individuals: Drinker Nondrinker Smoker 193 89 Nonsmoker 165 153 Which of the following statements is true? (a) The appropriate alternative hypothesis is Ha: Smoking and alcohol consumption are independent. (b) The appropriate null hypothesis is H0: Smoking and alcohol consumption are not independent. (c) The calculated value of the test statistic is 3.84. (d) The calculated value of the test statistic is 7.86. (e) At level 0.01 we conclude that smoking and alcohol consumption are related. 1b Chapter 13 4 14AB 2a 3a 4d 5c 6a 7e 8e 9c 10c 11a 12a 13e 14c 15c 16d 17e Chapter 13 5 14AB