# BA215 Business Statistics Final exam

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?

A) distribution of sample proportion, when the population proportion is 0.11

B) distribution of sample proportion, when the population proportion is 0.25

C) both the same

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

A) smaller

B) larger

C) the same

3.

The shape of the distribution of sample proportion is approximately normal. If the sample size were decreased to 22, the shape would be

A) less normal

B) more normal

C) the same

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?

A) 0.30

B) 140

C) 500

D)

140

500

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?

A) 16

B) 160

C) 16,000

6.

The shape of the distribution of sample proportion is approximately normal. The shape would be least normal for which of these sample sizes?

A) 16

B) 160

C) 16,000

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

300

1600

A) n

B) p

C) p̂

D) X

8.

The standard deviation for samples of 1600 students is 0.01. The standard deviation would be smallest for which of these sample sizes?

A) 16

B) 160

C) 16,000

9.

This graph shows the distribution of ACT scores for a population of students.

Which of these is your best guess for the probability of a score being greater than 30?

A) 0.016

B) 0.036

C) 0.16

D) 0.36

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.

A newborn with a length of 20 inches is

A) not at all unusual

B) somewhat unusual

C) extremely unusual

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:

Use the sketch of the tails of the z curve to estimate the probability of a BMI below 17:

between:

A) 0 and 0.005

B) 0.005 and 0.01

C) 0.01 and 0.025

D) 0.025 and 0.05

E) 0.05 and 1

12.

Probabilities of scores on a 10-point quiz for a group of students are shown below.

Score 4 5 6 7 8 9 10

Probability 0.04 0.06 0.12 0.30 0.30 0.14 0.04

Which of these is the median score?

A) 7

B) 7.5

C) 8

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

A) s

B) σ

C) x̄

D) μ

E) p̂

F) p

G) n

14.

In 1999, salaries of physician’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:

A) a parameter denoted s

B) a parameter denoted σ

C) a statistic denoted s

D) a statistic denoted σ

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.

Year 1 2 3 4

Probability 0.5 0.3 0.1 0.1

The distribution is

A) left-skewed

B) right-skewed

C) symmetric but not normal

D) approximately normal

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?

A) Check that there is no bias in the sampling or study design.

B) Check that the population is at least 10 times the sample size.

C) Check that there are should be at least 10 in and out of the category of interest (speaking another language at home).

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?

A) p

B) p̂

C)

p0

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?

A) yes

B) no

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

A) extreme

B) not extreme

C) borderline

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.

A) a Type I Error

B) a Type II Error

C) both (a) and (b)

D) neither (a) nor (b)

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?

A) use a lower level of confidence

B) use a smaller sample

C) both (a) and (b)

D) neither (a) nor (b)

22.

Which of the following would invalidate our confidence interval and subsequent conclusions?

A) If the 600 sampled youths were not representative of all youths in terms of their vision.

B) If the 600 sampled youths did not respond accurately to the question about vision impairment.

C) Both (a) and (b).

D) Neither (a) nor (b).

Points Earned: 2.0/2.0

23.

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?

A) 0.27

B) 270

C) 1000

D) none of the above

24.

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 α = 0.05 level?

A) 0

B) 4

C) 8

D) 28

E) 52

F) 72

G) 76

H) 80

25.

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

A) much wider

B) slightly wider

C) slightly narrower

D) much narrower

26.

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.

The mean and standard deviation are obtained from a representative sample of 9 undergrads; the data set has a normal appearance.

A) Use a z procedure: the P-value is small if z < -2.326.

B) Use a t procedure: the P-value is small if t < -2.896.

C) Neither z nor t is appropriate in this situation.

27.

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.]

A representative sample of 90 undergrads produces a standardized sample mean of t = -2.5; there are outliers in the data set.

A) We do not have convincing evidence that the population mean is less than 15.

B) There is convincing evidence that the population mean is less than 15.

C) No conclusions should be drawn because neither z nor t procedures are appropriate in this

Points Earned: 2.0/2.0

28.

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.

N Mean StDev SE Mean

MT1 15 122.13 18.91 4.88

MT2 15 110.20 20.19 5.21

Difference 15 11.93 9.25 2.39

95% lower bound for mean difference: 7.73

T-Test of mean difference = 0 (vs > 0): T-Value = 5.00 P-Value = XXXXX

The P-value has been X-ed out. Based on the size of the t statistic, the P-value is

A) small

B) not small

C) borderline

D) not enough info

29.

For a sample of 20 students, a test compared their first and second midterm exam scores.

N Mean StDev SE Mean

MT1 20 114.85 17.67 3.95

MT2 20 111.65 15.15 3.39

Difference 20 3.20 16.17 3.61

T-Test of mean difference = 0 (vs not = 0): T-Value = XXX P-Value = 0.387

If we test to see if the mean of differences for all students is positive, would we reject the null hypothesis?

A) yes

B) no

C) borderline

Points Earned: 2.0/2.0

30.

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.

N Mean StDev SE Mean

Treatment 16 585 90 22.5

Control 16 533 65 16.25

Difference = mu Treatment – mu Control

Estimate for difference: 52

95% CI for difference: (–4.7, 108.7)

T-Test of difference = 0 (vs >): T-Value = XXXX P-Value = 0.04 DF = 30

This was a

A) paired study

B) two-sample study

Points Earned: 2.0/2.0

31.

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?

A) yes

B) no – answer

Points Earned: 2.0/2.0

32.

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.

N Mean StDev SE Mean

Exports 8 25.63 14.40 5.09

Imports 8 15.75 9.51 3.36

Difference 8 9.88 12.91 4.56

95% CI for mean difference: (-0.93, 20.68)

T-Test of mean difference = 0 (vs not = 0): T-Value = 2.16 P-Value = 0.067

This was a

A) paired study – answer

B) two-sample study

33.

Percentages of roads classified as bad in 2006 were compared for a sample of 11 northern cities and a sample of 4 southern cities.

Location N Mean StDev SE Mean

north 11 62.2 12.1 3.7

south 4 49.0 17.8 8.9

Difference = mu (n) – mu (s)

Estimate for difference: 13.12

95% lower bound for difference: –7.33

T-Test of difference = 0 (vs >): T-Value = 1.37 P-Value = 0.12 DF = 4

Considering the size of the P-value for the two-sided alternative, would a 95% confidence interval for the difference between population means contain zero? (No calculations necessary.)

A) Yes, definitely.

B) No, not even close.

C) Borderline: either just barely or not quite.

D) There is not enough information to decide.

34.

A student compared tuition, in thousands of dollars, for samples of public and private colleges/universities in the U.S.

N Mean StDev SE Mean

Public 5 7.26 1.48 0.66

Private 6 32.32 3.30 1.3

Difference = mu Public – mu Private

Estimate for difference: –25.06

T-Test of difference = 0 (vs not =): T-Value = XXXX P-Value = 0.000 DF = 7

This was a

A) paired study

B) two-sample study – answer

35.

Short-term parking rates were compared for a sample of 11 parking lots in a city’s downtown area, in 2007 vs. 2008.

N Mean StDev SE Mean

2007 11 7.77 4.43 1.34

2008 11 -0.636 1.002 0.302

Difference 11 -0.636 1.002 0.302

T-Test of mean difference = 0 (vs not = 0): T-Value = –2.11 P-Value = 0.062

The design was

A) paired

B) two-sample

C) several sample

36.

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.

First compare the histograms’ centers: when were the densities higher on average?

A) before logging

B) after logging

37.

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:

Sample standard deviations are

A) relatively close

B) quite different

38.

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:

As far as the sample means are concerned, which group of students slept the longest?

A) first year

B) second year

C) third year

D) fourth year

E) other

39.

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?

A) the P-value is small

B) the P-value is not small – answer

40.

Miles driven (in thousands) were regressed on year for a sample of used Ford Mustangs.

The regression equation is

Miles = 10453 – 5.20 Year

Predictor Coef SE Coef T P

Constant 10453 1256 8.32 0.000

Year -5.2007 0.6261 -8.31 0.000

S = 8.629 R-Sq = 64.5% R-Sq(adj) = 63.6%

Would a confidence interval for the slope contain zero?

A) yes

B) no

41.

Prices of a sample of generic drugs were regressed on the prices of the brand-name equivalents.

The regression equation is

Generic = –4.4 + 0.689 Brand

Predictor Coef SE Coef T P

Constant -4.37 16.11 -0.27 0.790

Brand 0.68872 0.08865 7.77 0.000

S = 22.87 R-Sq = 78.0% R-Sq(adj) = 76.7%

Predicted Values for New Observations

New Obs Fit SE Fit 95.0% CI 95.0% PI

1 105.14 5.37 (93.82, 116.46) (55.58, 154.70)

Values of Predictors for New Observations

New Obs Brand

1 159

The slope of the regression line for the relationship between all brand and generic prices is

A) 0.689

B) unknown, but almost surely positive

C) unknown, and it could easily be negative

42.

Which of these is true about the confidence interval (C.I.)?

A) It estimates the mean of all responses to a given explanatory value.

B) It estimates an individual response to a given explanatory value.

43.

A newspaper surveyed its readers about all of its comics, where possible responses were love it, hate it, or don’t care. The count of readers who responded “hate it” was regressed on the count who responded “love it” for a sample of 6 comics (Foxtrot, Zits, Blondie, Mary Worth, The Amazing Spider Man, and Family Circus).

The regression equation is

HateIt = 2346 – 0.583 LoveIt

Predictor Coef SE Coef T P

Constant 2346.4 235.3 9.97 0.001

LoveIt -0.58347 0.09585 -6.09 0.004

S = 254.7 R-Sq = 90.3% R-Sq(adj) = 87.8%

New Obs Fit SE Fit 95.0% CI 95.0% PI

1 479 141 (87, 872) (-329, 1288)

Values of Predictors for New Observations

New Obs LoveIt

1 3200

Output is shown when interval estimates are requested for the number of people hating a comic, if 3,200 people loved it. Which interval tells us a range of plausible values for number hating a particular comic that was loved by 3,200 people?

A) CI

B) PI – answer

44.

An annual state assessment test is a standards based criterion-referenced assessment used to measure a student’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.

In this exercise, you are to identify which one of the three reported regression results corresponds to each of the three scatterplots.

95% confidence interval for β1 for regression of % passing on mean (plot on the left)

A) (–0.78,–0.50)

B) (0.17, 0.20)

C) (0.30,+1.61)

45.

regression line for regression of % passing on mean (plot on the left)

A) ŷ = -194 + 0.188x

B) ŷ = -55.4 + 0.953x

C) ŷ = 77.1 – 0.639x

46.

spread s about the line for regression of % passing on mean (plot on the left)

A) 5.6

B) 12.8

C) 17.1

47.

spread s about the line for regression of % passing on participated (plot in the middle)

A) 5.6

B) 12.8

C) 17.1

48.

t statistic to test if β1 = 0 for regression of % passing on participated (plot in the middle)

A) –9.05

B) +2.90

C) +27.90

49.

Scientists believe people’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?

A) sample survey

B) experiment

C) observational study

50.

The explanatory variable is

A) quantitative

B) categorical

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