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Null Hypothesis - Business Statistics - Exam, Exams of Business Statistics

Sam Higginbottom Institute of Agriculture, Technology and SciencesBusiness Statistics

This is the Past Exam of Business Statistics which includes Residual, Diameter, Fitted Regression, Predicts, Volume, Diameter and Height, Largest Residual, Residual Standard Deviation, Model Fit etc. Key important points are: Null Hypothesis, Distribution, Construct, Degrees of Freedom, Value, Hypothesis, Consumer Reports, Statistically Significant, Rejected, Process

Typology: Exams

2012/2013

Uploaded on 02/26/2013

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22S:008 Final Exam, May 12, 2000 Name:_______________________________
Form A ID: _______________________________________
Please circle one. Discussion Section: 9:30, 10:30, 11:30, or 12:30
Please enter all of your answers on these exam pages. There are 50 questions.
The Defective Question Report, Formula sheet, and Tables will be handed out separtely.
1. Consider a t-distribution with 15 degrees of freedom. Which of the following is the value we look up in the
t-distribution table to construct a 99% confidence interval for µ?
A) 2.602
B) 2.624
C) 2.947
D) 2.977
E) 3.000
2. Consider testing the null hypothesis H0: µ = 50. True or false? The test statistic is called the
t-statistic.
A) True B) False
3. In the beer-tasting example, Consumer Reports said “Although the 11 correct choices were an improvement
over guesswork, we don’t consider that to be statistically significant evidence that a beer drinker can tell
domestic Lowenbrau from Miller High Life.” True or false: This means they rejected the null hypothesis.
A) True B) False
4. If a process is stable (that is, in control), the process will produce goods or services that meet the customers’
specifications.
A) True B) False
5. Failing to reject a true null hypothesis is a correct decision.
A) True B) False
6. A normal distribution has a mean of 100 and a standard deviation of 16. What percentage of the data values
lie above the value 108?
A) 31%
B) 69%
C) 95%
D) 99%
E) 99.7%
7. The probability of a Type II error (computed under the assumption that the null hypotesis is true) is called the
significance level of the statistical test.
A) True B) False
8. Sampling Error is the difference between the value of a sample estimate and the corresponding value in the
population that is due to misleading and ambiguous questions.
A) True B) False
ny50–
()σ⁄()
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Download Null Hypothesis - Business Statistics - Exam and more Exams Business Statistics in PDF only on Docsity!

22S:008 Final Exam, May 12, 2000 Name:_______________________________

Form A ID: _______________________________________

Please circle one. Discussion Section: 9:30, 10:30, 11:30, or 12:

Please enter all of your answers on these exam pages. There are 50 questions. The Defective Question Report, Formula sheet, and Tables will be handed out separtely.

  1. Consider a t -distribution with 15 degrees of freedom. Which of the following is the value we look up in the t -distribution table to construct a 99% confidence interval for μ? A) 2. B) 2. C) 2. D) 2. E) 3.
  2. Consider testing the null hypothesis H 0 : μ = 50. True or false? The test statistic is called the t-statistic. A) True B) False
  3. In the beer-tasting example, Consumer Reports said “Although the 11 correct choices were an improvement over guesswork, we don’t consider that to be statistically significant evidence that a beer drinker can tell domestic Lowenbrau from Miller High Life .” True or false: This means they rejected the null hypothesis. A) True B) False
  4. If a process is stable (that is, in control), the process will produce goods or services that meet the customers’ specifications. A) True B) False
  5. Failing to reject a true null hypothesis is a correct decision.

A) True B) False

  1. A normal distribution has a mean of 100 and a standard deviation of 16. What percentage of the data values lie above the value 108? A) 31% B) 69% C) 95% D) 99% E) 99.7%
  2. The probability of a Type II error (computed under the assumption that the null hypotesis is true) is called the significance level of the statistical test. A) True B) False
  3. Sampling Error is the difference between the value of a sample estimate and the corresponding value in the population that is due to misleading and ambiguous questions. A) True B) False

n ( ( y – 50 ) ⁄σ)

  1. The distribution of a sample statistic over all possible samples is called a sampling distribution.

A) True B) False

  1. The set of all measurements on a variable in a universe is called a population.

A) True B) False

  1. Tampering with a process that is in statistical control will usually increase the variability in the process.

A) True B) False

  1. Consider 4 Bernoulli trials with success probability π = 0.2. Which of the following gives the probability of observing at least three successes? A) (0.2)^4 B) 4(0.2)^3 (0.8) C) 4(0.2)^3 (0.8) + (0.2)^4 D) (0.8)^4 E) 1 − (0.8)^4
  2. The graph at the below displays the Binomial distribution with 10 trials and success probability .5. A normal curve with the same mean and same standard deviation is also shown. The shaded area gives the normal approximation for the chance of A) exactly 7 successes using the continuity correction. B) 7 or more successes using the continuity correction. C) exactly 7 successes without using the continuity correction. D) 7 or more successes without using the continuity correction. E) exactly 7 successes with no approximation.
  3. Control charts reflect both the cross-sectional and longitudinal aspects of a process.

A) True B) False

  1. The standard deviation of the distribution of the number of successes in n trials of a Bernoulli process is largest when π = 0.5. A) True B) False
  2. In a simple random sample, increasing the sample size will increase the margin of sampling error (other things being equal). A) True B) False

0 1 2 3 4 5 6 7 8 9 10

Probability

Successes

  1. A company selected a random sample of 100 accounts receivable. For these accounts they calculated a mean of $340 and a standard deviation of $70. What is the lower endpoint of a 95% confidence interval for the mean of the population of all accounts receivable? (Assume a large population.) A) $ B) $ C) $ D) $ E) $
  2. A survey organization would like to estimate a population percentage in a large population to an accuracy of 5 percentage points with 95% confidence. They have no current knowledge of the size of the percentage. How large should a random sample be to acheive their goal for the margin of error? A) 100 B) 200 C) 400 D) 1100 E) None of the above.
  3. Five percent of the products produced by a certain stable process are defective. If a random sample of 4 items is taken, what is the probability that the sample contains at most one defective? (to the nearest hundredth) A) 0. B) 0. C) 0. D) 0. E) 0.
  4. Suppose that 30 subgroups (samples) each of size 50 are selected from a Bernoulli process. If there are 150 defectives overall, what is the value of the upper control limit (UCL) for the p -chart for fraction defective? (Rounded to the nearest hundredth.) A) 0. B) 0. C) 0. D) 0. E) 0.
  5. The regression model where x and is a continuous variable, and z is a binary indicator variable is best described as A) one straight line B) two parallel lines C) two non-parallel lines D) a quadratic curve E) a regression plane
  6. A statistic is a numerical characteristic of a sample.

A) True B) False

y ˆ^ = b 0 + b 1 x + b 2 z

  1. The Central Limit Effect applied to a sample proportion p from n trials of a Bernoulli process says that for large n the distribution of p is approximately normal with mean π and standard deviation. A) True B) False
  2. If data have a very strong upward but curved relationship, it is possible to get a correlation coefficient that is larger than +1. A) True B) False
  3. In general, the larger the residual standard deviation, the better the regression model.

A) True B) False

  1. Each year the General Social Survey, GSS, selects 1500 households throughout the U.S. using complicated randomization methods. People in the selected households are interviewed extensively to gather social science data. Such a study is best classified as A) a designed experiment with blinding of the subjects B) an observational study C) a designed study D) a double blind, designed experiment E) a designed experiment with neither blinding nor double blinding
  2. In the Physicians’ Health Study 22,000 male doctors were used as subjects to measure the effect of a simple drug in the prevention of heart attacks. In this study aspirin was used as a placebo. A) True B) False
  3. The Physicians’ Health Study used double blinding.

A) True B) False

  1. The Physicians’ Health Study failed to use randomization to decide which subjects received the real drug and which received the placebo. A) True B) False
  2. A prediction based on a regression line is likely to be very precise when

I. the residual sum of squares is small II. the residual standard deviation is small III. the value of R^2 is close to 100% A) I only B) II only C) III only D) I, II, and III E) None of the above

  1. In a perfectly symmetric distribution the distance from the first quartile to the median is the same as the distance from the median to the third quartile. A) True B) False

( π ( 1 – π)) ⁄ n

  1. Which of the following statistics are resistant to outliers?

I. The median II. The interquartile range III. The standard deviation A) I and II only B) I and III only C) II and III only D) I, II, and III E) None of the above.

  1. The table below gives the breakdown of shoe sale transactions over a long period for a large shoe chain. An auditor selects one transaction at random from all of the transactions.

What is the chance that a Credit Card transaction is selected? A) 20% B) 35% C) 55% D) 80% E) None of the above.

  1. The density histogram at the right displays the distribution of heights of the 220 males in a class. The mean is 71.3 inches. Which of the following values could be the standard deviation of the distribution? (Notice that the distribution is quite mound-shaped.) A) 1. B) 2. C) 7. D) 11. E) 15.
  2. If you are interested in predicting future behavior of a meandering process , it would be more helpful to look at a histogram of the data rather than a sequence plot. A) True B) False

Brand Purchased Reebok Nike Other Type of Purchase

Cash 5% 10% 5% Credit Card 40% 15% 25%

60 70 80

Height

Density

Heights of Males in 22S:

  1. A regression model was used to explain young girls’ Heights (in inches) from their Age (in years). The Minitab results are shown below. The regression equation is Height = 27.6 + 2.58 Age Predictor Coef StDev T P Constant 27.6242 0.6716 41.13 0. Age 2.58424 0.08163 31.66 0. S = 1.349 R-Sq = 98.7% R-Sq(adj) = 98.6% Analysis of Variance Source DF SS MS F P Regression 1 1824.7 1824.7 1002.20 0. Residual Error 13 23.7 1. Total 14 1848. From this regression output we see that the residual standard deviation is A) 1. B) 1. C) 23. D) 1848. E) None of the above.
  2. Refer to question 48. From this regression output we see that the least-squares slope coefficient is

A) 1. B) 2. C) 23. D) 27. E) 98.7%

  1. Refer to question 48. True or false: From this regression output we see that the model is slightly better if we do not adjust the R^2 value. A) True B) False