Midterm Math

An SRS of 45 male employees at a large company found that 36 felt that the company was supportive of female and minority employees. An independent SRS of 40 female employees found that 24 felt that the company was supportive of female and minority employees. Let p1 represent the proportion of all male employees members at the company and p2 represent the proportion of all female employees members at the company who hold this opinion. We wish to test the hypotheses nar021-1.jpg vs. nar021-2.jpg

0.8 - 0.6 / (0.706)(0.294)/45

Use Scenario 11-7. Which of the following may we conclude, based on the test results?

There is not much evidence of an association between wiring configuration and the type of cancer that caused the deaths of children in the study.

Does room temperature affect cognitive function? A psychologist randomly divides 60 volunteers into two groups. One group of 30 solves a crossword puzzle in a room kept at 72 Fº, the other group of 30 solves the puzzle in a room kept at 85 Fº. The mean completion time nar024-1.jpg for the subjects in the "cool" room is 20 minutes and the standard deviation is nar024-2.jpg= 6 minutes. The mean nar024-3.jpg for the subjects in the "warm" room is 26 minute and the standard deviation is nar024-4.jpg= 8 minutes. Let nar024-5.jpg and nar024-6.jpg represent the mean completion times for all potential volunteers similar to the ones in this study when they are in "cool" or "warm" rooms, respectively.

(-11.01, -0.99)

An ambitious reporter for a large university newspaper suspects that Mr. Hazzard, a new statistics teacher, is grading his introductory statistics students too harshly. From school records the reporter determines that over the past 2 years the proportions of students in all sections of introductory statistics (taught by many different teachers) received grades of A, B, C, D, or F in the following proportions: A: 0.20; B: 0.30; C: 0.30; D: 0.10; and F: 0.10. The reporter then takes an SRS of 90 students who took introductory statistics with Mr. Hazzard in the past two years and gathers the following information:

(0.10)(90)

According to recent polls, 21% of people in the United States answered Yes to the question, "Did you smoke any form of tobacco yesterday?" In the European Union, 27% of people answered yes to a similar question. Let's assume these are population parameters for the two populations. If you select a simple random sample of 40 people in the U.S. and 50 people in the E.U., which of the following expressions represents the standard deviation of the sampling distribution for the difference in the proportion of smokers in the two groups?

(0.2)(0.79)/40 + (0.27)(0.73)/50

A random sample of 200 Canadian students were asked about their hand dominance and whether they suffer from allergies. Here are the results:

(20)(118)/200

Ida wants to know if males and females prefer different brands of ready-made chocolate-chip cookie dough. She bakes eight dozen cookies from dough made by each of four manufacturers which she labels brands A, B, C, and D. She then selects a simple random sample of 96 students, records their gender, gives them one cookie of each brand and asks which brand they like best. Here are her results: Use Scenario 11-5. The expected count for the cell "Males/Brand B" cell is given by which of the following expressions?

(38)(18)/96

researcher wished to test the effect of the addition of extra calcium to yogurt on the "tastiness" of yogurt. Sixty-two adult volunteers were randomly divided into two groups of 31 subjects each. Group 1 tasted yogurt containing the extra calcium. Group 2 tasted yogurt from the same batch as group 1 but without the added calcium. Both groups rated the flavor on a scale of 1 to 10, with 1 being "very unpleasant" and 10 being "very pleasant." The mean rating for group 1 was nar023-1.jpg with a standard deviation of nar023-2.jpg. The mean rating for group 2 was nar023-3.jpg with a standard deviation of nar023-4.jpg. Letnar023-5.jpg and nar023-6.jpg represent the mean ratings we would observe for the entire population represented by the volunteers if all members of this population tasted, respectively, the yogurt with and without the added calcium.

. It would be narrower.

Are avid readers more likely to wear glasses than those who read less frequently? Three hundred men in the Korean army were selected at random and classified according to whether or not they wore glasses and whether the amount of reading they did was above average, average, or below average. The results are presented in the following table. The chi-square statistic for this test would have a mc089-1.jpg distribution with how many degrees of freedom?

2

Some researchers have conjectured that stem-pitting disease in peach tree seedlings might be controlled with weed and soil treatment. An experiment was conducted to compare peach tree seedling growth with soil and weeds treated with one of two herbicides. In a field containing 20 seedlings, 10 were randomly selected from throughout the field and assigned to receive Herbicide A. The remaining 10 seedlings were to receive Herbicide B. Soil and weeds for each seedling were treated with the appropriate herbicide, and at the end of the study period, the height (in centimeters) was recorded for each seedling. A box plot of each data set showed no indication of non-Normality. The following results were obtained:

3.43

Use Scenario 11-6. Suppose we wish to test the null hypothesis that there is no association between the amount of reading you do and whether or not you wear glasses. Under the null hypothesis, which of the following is the expected number (approximately) of above-average readers who wear glasses?

30.7

Use Scenario 11-6. The conditional distribution of the variable "Wear Glasses" for Average readers (in percents) is:

38.1%; 61.9%

Use Scenario 11-6. Suppose we wished to display in a graph the proportion of all above-average readers who wear glasses and do not wear glasses, respectively. Which of the following graphical displays is best suited to this purpose?

A bar graph

Ida wants to know if males and females prefer different brands of ready-made chocolate-chip cookie dough. She bakes eight dozen cookies from dough made by each of four manufacturers which she labels brands A, B, C, and D. She then selects a simple random sample of 96 students, records their gender, gives them one cookie of each brand and asks which brand they like best. Here are her results: Use Scenario 11-5. The appropriate null hypothesis for Ida's question in this problem is:

Gender and cookie brand are independent.

Random samples of male and female high school students were asked to identify their favorite food group. Here are the results:

Male/protiens

A researcher wished to test the effect of the addition of extra calcium to yogurt on the "tastiness" of yogurt. Sixty-two adult volunteers were randomly divided into two groups of 31 subjects each. Group 1 tasted yogurt containing the extra calcium. Group 2 tasted yogurt from the same batch as group 1 but without the added calcium. Both groups rated the flavor on a scale of 1 to 10, with 1 being "very unpleasant" and 10 being "very pleasant." The mean rating for group 1 was nar023-1.jpg with a standard deviation of nar023-2.jpg. The mean rating for group 2 was nar023-3.jpg with a standard deviation of nar023-4.jpg. Letnar023-5.jpg and nar023-6.jpg represent the mean ratings we would observe for the entire population represented by the volunteers if all members of this population tasted, respectively, the yogurt with and without the added calcium.

None of the things described in the above four choices would invalidate t-procedures.

Do certain car colors attract the attention of police more than others, so that they are more likely to get speeding tickets? A few years ago a curious newspaper columnist tabulated the car color on a random sample of 120 speeding citations at the local courthouse. Here are his results. Color Red White/Silver Gray/Black Other

Red: 16.8 White/Silver: 42.0 Grey/Black: 27.6 Other: 33.6

Do certain car colors attract the attention of police more than others, so that they are more likely to get speeding tickets? A few years ago a curious newspaper columnist tabulated the car color on a random sample of 120 speeding citations at the local courthouse. Here are his results.

Reject H0 at the mc084-6.jpg = 0.10 level: there is evidence that certain car colors get more speeding tickets than others.

An agricultural researcher wishes to see if a kelp extract helps prevent frost damage on tomato plants. One hundred tomato plants in individual containers are randomly assigned to two different groups. Plants in both groups are treated identically, except that the plants in group 1 are sprayed weekly with a kelp extract, while the plants in group 2 are not. After the first frost in the autumn, 12 of the 50 plants in group 1 exhibited damage, and 18 of the 50 plants in group 2 showed damage. Let p1 be the actual proportion of all tomato plants of this variety that would experience damage under the kelp treatment, and let p2 be the actual proportion of all tomato plants of this variety that would experience damage under the no-kelp treatment, assuming that the tomatoes are grown under conditions similar to those in the experiment.

between 0.05 and 0.10

If each observed count is exactly equal to each expected count in a chi-square goodness-of-fit test, then the chi-square statistic will

equal 0.

A radio show runs a phone-in survey each morning. One morning the show asked its listeners whether they would prefer Congress or the president to set policy for the nation. The majority of those phoning in their responses answered "Congress," and the station reported the results as statistically significant. We may safely conclude that

he majority of those phoning in their responses prefer Congress to set policy for the nation, but know very little about anyone else.