# BA 215 BA215 Final Exam Answers (Grantham)

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BA 215 Final Exam (Grantham)

1. Experts have estimated that 25% of all homeless people in the U.S. are veterans. The proportion of Americans in general who are homeless is 0.11. For random samples of 100 people, which is more normal?
2. Many biologists and anthropologists claim that 10 percent of all children conceived in the context of a marriage have been fathered by someone from outside the couple. In this situation, the standard deviation for samples of 225 births is 0.02. If the sample size were decreased, the standard deviation would be
3. The shape of the distribution of sample proportion is approximately normal. If the sample size were decreased to 22, the shape would be
4. The probability of birth by Caesarean in the U.S. is 0.30.If the probability of Caesarean birth is 0.30, and 140 in a sample of 500 births are Caesarean, which of these numbers is X?
5. The probability of being a smoker for a population of college students is 0.20.The standard deviation for samples of 1600 students is 0.01. The standard deviation would be smallest for which of these sample sizes?
6. The shape of the distribution of sample proportion is approximately normal. The shape would be least normal for which of these sample sizes?
7. Suppose 300 in a sample of 1600 students smoke, whereas the population proportion smoking is 0.20. What notation do we use for the number
8. The standard deviation for samples of 1600 students is 0.01. The standard deviation would be smallest for which of these sample sizes?
9. This graph shows the distribution of ACT scores for a population of students.
10. Lengths of newborn babies (in inches) have a mean of 20 and a standard deviation of 2. Once z-scores are found, this sketch of the tails of the normal curve can be used to estimate probabilities.
11. Pre-pregnancy BMI for a population of women is approximately normal with a mean of 24 and a standard deviation of 4. Use the sketch of the tails of the z curve to estimate the probability of a BMI below 17:
12. Probabilities of scores on a 10-point quiz for a group of students are shown below.
13. Lifespans of male mice have a mean of 860 days and a standard deviation of 40 days. The shape of the distribution is moderately skewed to the left.If we take a sample of mice from this population, how do we denote the mean of their lifespans
14. In 1999, salaries of physicianās assistants in the U.S. had a mean of 68.0 thousand and a standard deviation of 17.0 thousand. The shape of the distribution may have some skewness.In this problem, the number 17 is:
15. Year-level for a population of undergraduate introductory statistics students had probability distribution shown below; the mean level was 1.8 and the standard deviation was 1.0.
16. The proportion of Americans over the age of five who speak another language besides English at home is 0.20. Suppose we take a random sample of 64 Americans over the age of five.Which one of these do we check in order to justify our claim for the mean of the distribution of sample proportion?
17. Online interviews of 1500 parents with children under the age of eight found the proportion who read to their children at least twenty minutes daily to be 0.78. Suppose a reporter would like to claim that more than three-fourths (0.75) of all parents with children under eight read to them at least twenty minutes daily.What notation do we use for the number 0.75?
18. Based on the data provided, can the reporter conclude that more than 0.75 of all parents with children under eight read to them at least twenty minutes daily?
19. The national rate of binge drinking among eighth graders is assumed to be 0.10. We would like to see if the rate of binge drinking among eighth graders in a particular state differs significantly from the national rate. In a survey of 4000 eighth graders from that state, the proportion who reported binge drinking in the previous month was 0.07.The size of the z-statistic is
20. A Type I Error is rejecting the null hypothesis, even though it is true; a Type II Error is failing to reject the null hypothesis, even though it is false.
21. Recently a sample of 250 taxicab drivers in Massachusetts were observed; 17 of them were using seatbelts.How could we obtain a narrower interval?
22. Which of the following would invalidate our confidence interval and subsequent conclusions?
23. Ā
In a 2006 poll of 1000 Americans, the proportion who were satisfied with the way things were going in the U.S. was only 0.27.Which of these is denoted by X in this situation?
24. Ā
Each student in a class of 80 rolls 8 dice in order to perform inference about the mean of all dice rolls (which happens to be 3.5).Suppose each student uses his or her sample to test the true null hypothesis that the population mean is 3.5 against the two-sided alternative. About how many of these 80 tests should reject at the Ī± = 0.05 level?
25. Ā
Suppose that 6 minutes had been the sample standard deviation. Use the fact that the t multiplier for 35 degrees of freedom and 95% confidence is 2.03 to consider a confidence interval for the population mean REM sleep time. Compared to the z interval, the t interval would be
26. Ā
For this problem, we will assume that the null hypothesis should be rejected as long as the P-value is less than 0.01. (Note that the area under the t curve for 8 degrees of freedom to the left of -2.896 is 0.01.) Suppose the mean and standard deviation for number of credits taken in a semester by a sample of undergrads are used to test whether the mean credits taken by all undergrads is less than 15. Choose the correct approach under each of the following circumstances. The mean and standard deviation are obtained from a representative sample of 9 undergrads; the data set has a normal appearance.
27. Ā
For this problem, we will assume that the null hypothesis should be rejected as long as the P-value is less than 0.01. Suppose the mean and standard deviation for number of credits taken in a semester by a sample of undergrads are used to test whether the mean credits taken by all undergrads is less than 15. Choose the correct conclusion under each of the following circumstances: [You may refer either to the sketch of the t distribution for 8 degrees of freedom, or to the standard normal (z) curve.]
28. Ā
Based on first and second midterm exam scores for a sample of students, a test is carried out to see if in general students tend to do worse on the second midterm exam.
29. Ā
For a sample of 20 students, a test compared their first and second midterm exam scores.
30. Ā
An experiment compared reaction times in a driving simulation for a control group (who listened passively to an audio book) with a treatment group (who were obliged to converse using a hands-free cell phone). Software produced the following output.
31. Ā
If we test to see if overall reaction times were longer for the cell phone group, and use = 0.01 as the cutoff for a small P-value, would we reject the null hypothesis and conclude the difference between means is greater than zero?
32. Ā
A survey for business owners, conducted on a sample of 8 countries, looked at the percentage of businesses in each country that exported goods to China, and the percentage that imported goods from China. Output is shown from carrying out a comparison with software.
33. Ā
Percentages of roads classified as bad in 2006 were compared for a sample of 11 northern cities and a sample of 4 southern cities.
34. Ā
A student compared tuition, in thousands of dollars, for samples of public and private colleges/universities in the U.S.
35. Ā
Short-term parking rates were compared for a sample of 11 parking lots in a cityās downtown area, in 2007 vs. 2008.
36. Ā
A masters thesis by M. Purser at the University of Washington in 1988 looked at soil densities in a conifer forest, before and after clearcut logging in the area. These histograms show 32 pre-logging densities and 38 post-logging densities, recorded in grams per cubic centimeter. Unlike most before-and-after designs, this was a two-sample study: the same sample of soil could not be assessed twice.
37. Ā
Is there a difference in mean hotel rates (five-night stay) for all hotels in Jamaica Curacao, and St. Lucia? Analysis of variance was carried out on samples of hotels a each of the three resorts:
38. Ā
Is there a difference in mean hours slept for students in various years (1, 2, 3, 4, or other) at college? Analysis of variance was carried out on survey data from several hundred students at a certain university:
39. Ā
Prices for samples of 16 new fiction, 16 non-fiction, and 10 advice books (all hardcover) were compared to determine if the overall mean price could be the same for the three types of book.The mean of any F curve is close to 1. What does the size of your F statistic suggest about the size of the P-value?
40. Ā
Miles driven (in thousands) were regressed on year for a sample of used Ford Mustangs.
41. Ā
Prices of a sample of generic drugs were regressed on the prices of the brand-name equivalents.
42. Ā
Which of these is true about the confidence interval (C.I.)?
43. Ā
A newspaper surveyed its readers about all of its comics, where possible responses were love it, hate it, or donāt care. The count of readers who responded āhate itā was regressed on the count who responded ālove itā for a sample of 6 comics (Foxtrot, Zits, Blondie, Mary Worth, The Amazing Spider Man, and Family Circus).
44. Ā
An annual state assessment test is a standards based criterion-referenced assessment used to measure a studentās attainment of the academic standards while also determining the degree to which school programs enable students to attain proficiency of the standards. For a sample of schools, three relationships are considered: percentage passing versus school mean score, percentage passing versus percentage who participated (took the test) in each school, and percentage passing versus percentage of disadvantaged students in the school.
45. Ā
regression line for regression of % passing on mean (plot on the left)
46. Ā
spread s about the line for regression of % passing on mean (plot on the left)
47. Ā
spread s about the line for regression of % passing on participated (plot in the middle)
48. Ā
t statistic to test if Ī²
1 = 0 for regression of % passing on participated (plot in the middle)
49. Ā
Scientists believe peopleās ears get larger with age. They measured ear length in a sample of patients, aged 30 to 93, and found their ears grew about 0.01 inches a year.What type of study was this?
50. Ā
The explanatory variable is

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