Probability & Statistics



AP Statistics Name ______________________________________

Review: Chi-Square

Part I. Perform the following tests.

1. A study is being conducted to determine whether there is a relationship between jogging and blood pressure. A random sample of 210 subjects is selected, and they are classified as shown in the table. At ( = 0.05, test the claim that jogging and blood pressure are not related.

2. A staff member of an emergency medical service wishes to determine whether the number of accidents is equally distributed during the week. A week was selected at random, and the following data were obtained. Is there evidence to reject the hypothesis that the number of accidents is equally distributed throughout the week, at ( = 0.05?

3. Shopping at secondhand stores is becoming more popular and has even attracted the attention of business schools. A study of customers’ attitudes toward secondhand stores interviewed samples of shoppers at two secondhand store of the same chain in two cities. The breakdown of the respondents by sex is shown below. Is there a significant difference between the proportions of women customers in the two cities?

4. The chair of the history department of a college hypothesizes that the final grades are distributed as 40% A's, 30% B's, 20% C's, 5% D's and 5% F's. At the end of the semester, the following numbers of grades were earned. For ( = 0.05, is the grade distribution for the department different from that expected?

5. A survey of the 164 state representatives is conducted to see whether their opinions on a bill are related to their party affiliation. The following data are obtained. At ( = 0.01, can the researcher conclude that opinions are related to party affiliations?

Part II. Identify the type of chi-square test shown below and state the hypotheses.

6. The concessions manager at Twin Rivers Stadium wishes to see whether there is any preference in the flavors of popcorn that are sold during sporting events. A random sample of sales is selected, and the data are shown below. At ( = 0.01, are the flavors selected with equal frequency?

7. A recent Gallup poll asked the same question that has been asked every year for many years: “What do you think is the most important problem facing this country today?” The responses are shown below for the three major concerns over the years 1995 to 1998. Are the proportions for the problems the same for each year?

8. A researcher wishes to determine if on-line service or Internet use is independent of user. A sample of 300 computer users shows the following data. At ( = 0.10, can the researcher conclude that usage is independent of the user?

9. The American Red Cross reports that 42% of Americans have type 0 blood, 44% have type A blood, 10% have type B blood, and 4% have type AB blood. A county medical examiner hypothesizes the distribution of blood types is the same in his county as it is nationally. A random sample of 200 people is selected, and the following data are tallied. At ( = 0.10, can the examiner conclude that his hypothesis is correct?

10. A children's playground equipment manufacturer read in a survey that 55% of all American playground injuries occur on the monkey bars. The manufacturer wishes to investigate playground injuries in four different parts of the country to determine if the proportions of accidents on the monkey bars are equal. The results from randomly selected samples are shown below. At ( = 0.01, test the claim that the proportions are equal.

Part III. For each of the following, state the formula that you would use. If it’s a hypothesis test give the hypotheses and state the value of the test statistic and p-value. If it’s a confidence interval then state the interval.

11. A telephone company representative estimates that 40% of its customers want call-waiting. To test this hypothesis, she selected a sample of 250 customers and found that 37% had call waiting. At a 1% significance, is her estimate appropriate?

12. If you bought a used camera in good condition from a friend, would you pay the same as you would if you bought the same item from a stranger?

13. A sample of 35 assistant professors had a mean salary of $43,260 with a standard deviation of $5230 and 40 professors had a mean salary of $65,870 with a standard deviation of $5890. Find a 99% confidence interval for the mean difference in the salaries of assistant professors and professors.

14. In a sample of 80 Americans, 62 wished that they were rich. In a sample of 90 Europeans, 56 wished that they were rich. Find and interpret the 95% confidence interval for the difference of the two proportions.

15. A researcher wishes to estimate the average age of lifeguards is Ocean City. She selects a sample of 26 guards and finds the mean of the sample to be 24.7, with a standard deviation of 2 years. Find a 95% confidence interval.

16. The AMA wants to test the idea that general practitioners are more in favor of government controlled health care reform. In a sample of 200 surgeons, they found that 15% thought the government should control health care. In a sample of 200 general practitioners, 21% felt this way.

17. A dietitian wishes to see if a person’s cholesterol level will change if the diet is supplemented by a mineral. Can it be concluded that the cholesterol level has changed? Construct a 90% confidence interval.

|Subject |1 |2 |3 |4 |5 |6 |

|Before |210 |235 |208 |190 |172 |244 |

|After |190 |170 |210 |188 |173 |228 |

18. The Medical Rehabilitation Foundation reports that the average cost of rehabilitation for stroke victims is $24,672. To see if the average cost of rehabilitation is different at a large hospital, a researcher selected a random sample of 35 stroke victims and found that the average cost of their rehabilitation is $25,266. The standard deviation is $3,251. Use a 1% significance level.

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| | |Blood Pressure |

|Jogging Status |Low |Moderate |High |

|Joggers |34 |57 |21 |

|Non-joggers |15 |63 |20 |

|Day |Mon. |Tues. |Wed. |Thurs. |Fri. |Sat. |Sun |

|# accidents |28 |32 |15 |14 |38 |43 |19 |

|  |City A |City B |

|Men |38 |68 |

|Women |203 |150 |

|Grade |A |B |C |D |F |

|Number |45 |52 |39 |8 |6 |

| | |Opinion | |

|Party |Approve |Disapprove |No opinion |

|Republican |27 |15 |13 |

|Democrat |43 |18 |12 |

|Independent |9 |15 |12 |

|Flavor |Plain |Barbecue |Butter |Cheddar |

|# sold |25 |18 |32 |45 |

|  |Jobs |Crime |Health Care |Other |

|1998 |110 |200 |60 |630 |

|1997 |180 |200 |60 |560 |

|1996 |200 |250 |80 |470 |

|1995 |210 |250 |70 |470 |

| |Service Usage | |

| |Increase |Same |Decrease |

|Business |79 |21 |10 |

|Consumer |122 |63 |15 |

|Type |O |A |B |AB |

|Frequency |58 |65 |55 |22 |

| |North |South |East |West |

|On Monkey Bars |15 |18 |13 |16 |

|Not on Monkey Bars |15 |12 |17 |14 |

| |30 |30 |30 |30 |

|Friend |275 |300 |260 |300 |255 |275 |290 |

|Stranger |260 |250 |170 |130 |200 |225 |240 |

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