# Business Statistics – BA 215 FINAL EXAM QUESTIONS

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 0.11B) Distribution of sample proportion, when the population proportion is 0.25C) Both the same

2. 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 normalB) More normalC) The same

3. 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) 0.30B) 140C) 500D) 140/500

4. Suppose 300 in a sample of 1600 students smoke, whereas the population smoking is 0.20. What notation do we use for the number 300/1600.

A) NB) PC) p?D) X

5. 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 0.005B) 0.005 and 0.01C) 0.01 and 0.025D) 0.025 and 0.05E) 0.05 and 1

6. 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) SB) AC) x?D) ?E) p?F) pG) n

7. In 1999, salaries of physicians 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 sB) A parameter denoted ?C) A statistic denoted sD) A statistic denoted ?

8. 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 4Probability 0.5 0.3 0.1 0.1

A. Left-skewedB. Right-skewedC. Symmetric but not normalD. Approximately normal

9. 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).

10. 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) ExtremeB) Not extremeC) Borderline

11. 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 ErrorB) A Type II ErrorC) Both (A) and (B)D) Neither (A) and (B)

12. 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 confidenceB) Use a smaller sampleC) Both (A) and (B)D) Neither (A) or (B)

13. 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 ? = 0.05 level?

A) 0B) 4C) 8D) 28E) 52F) 72G) 76H) 80

14. 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 widerB) Slightly widerC) Slightly narrowerD) Much narrower

15. 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< -2.326B) Use a t procedure: the P-value is small if t< -2.896C) Neither z nor t is appropriate in this situation
16. 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 MeanMT1 15 122.13 18.91 4.88MT2 15 110.20 20.19 5.21Difference 15 11.93 9.25 2.3995% lower bound for mean difference: 7.73T-Test of mean difference = 0 (vs > 0): T-Value = 5.00 P-Value = XXXXXThe P-value has been X-ed out. Based on the size of the t statistic, the P-value isA) SmallB) Not smallC) BorderlineD) Not enough info

17. 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 Meannorth 11 62.2 12.1 3.7south 4 49.0 17.8 8.9Difference = mu (n) – mu (s)Estimate for difference: 13.1295% lower bound for difference: 7.33T-Test of difference = 0 (vs >): T-Value = 1.37 P-Value = 0.12 DF = 4Considering 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, definitelyB) No, not even closeC) Borderline: either just barely or not quiteD) There is not enough information to decide

N Mean StDev SE Mean2007 11 7.77 4.43 1.342008 11 -0.636 1.002 0.302Difference 11 -0.636 1.002 0.30218. Short-term parking rates were compared for a sample of 11 parking lots in a citys downtown area, in 2007 vs. 2008.

T-Test of mean difference = 0 (vs not = 0): T-Value = 2.11 P-Value = 0.062The design wasA) PairedB) Two-sampleC) Several sample

19. 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 yearB) Second yearC) Third yearD) Fourth yearE) Other

20. Prices of a sample of generic drugs were regressed on the prices of the brand-name equivalents.The regression equation isGeneric = 4.4 + 0.689 BrandPredictor Coef SE Coef T PConstant -4.37 16.11 -0.27 0.790Brand 0.68872 0.08865 7.77 0.000S = 22.87 R-Sq = 78.0% R-Sq(adj) = 76.7%Predicted Values for New ObservationsNew Obs Fit SE Fit 95.0% CI 95.0% PI1 105.14 5.37 (93.82, 116.46) (55.58, 154.70)Values of Predictors for New ObservationsNew Obs Brand1 159The slope of the regression line for the relationship between all brand and generic prices isA) 0.689B) Unknown, but almost surely positiveC) Unknown, and it could easily be negative

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