PART A

Question 1:

The following data represent the number of cases of salad dressing purchased per week by a local supermarket chain over a period of 30 weeks.

a. Construct an ordered stem and leaf display to sort the data.

b. After examining the stem and leaf display prepared in a., comment on the possible distribution of the number of cases purchased by the supermarket chain.

c. When the table of descriptive statistics was printed below, the ink in the printer was running low and many of the important descriptive statistics were missing. Find all these missing values.

d. Compare the mean and the median. Based on this comparison, what is the most likely distribution of the number of cases purchased? Explain.

e. If you had to make a prediction of the number of cases of salad dressing that would be ordered next week, how many cases would you predict? Why?

Question 2:

a. The probability that a consumer entering a retail outlet for microcomputers and software packages will buy a particular type of computer is 0.15. The probability that the consumer will buy a particular software package is 0.10. There is a 0.05 probability that the consumer will buy both the computer and the software package.

i. What is the probability that the consumer will buy the computer or the software package or both?

ii. If a consumer buys the particular type of computer, what is the probability he will also buy the software package?

b. An advertisement claims that two out of five doctors recommend a certain pharmaceutical product. A random sample of 20 doctors is selected, and it is found that only two of them recommend the product.

i. Assuming the advertising claim is true, what is the probability of the observed event?

ii. Assuming the claim is true, what is the probability of observing two or fewer doctors recommending the product?

iii. Given the sampling results, do you believe the advertisement? Explain.

c. Final grades in a university subject were normally distributed with an average of 68% and standard deviation of 12%.

i. If the pass mark was 50%, what proportion of the class failed?

ii. The lecturer in charge is instructed to award a credit grade to all students who scored 75% or more. What is the probability a randomly selected student will score a credit?

iii. The lecturer in charge is also instructed to award High Distinctions to at most, 10% of the class. What is the minimum cut-off grade for a HD?

Question 3:

a. The taxation department wants to estimate to within $500, the average income of all workers, with 95% confidence. How large a sample should the department take if the standard deviation for incomes is known to be $3000?

b. A sample of 25 male students from QBM 117 had their heights recorded. It was found that the average and standard deviation of their heights was 180cm and 5cm respectively.

i. Calculate a 95% confidence interval for the population average heights of males who attend QBM 117.

ii. From historical data it was found that the average height of males in QBM117 was 175cm. Is there reason to believe that there has been an increase in males height? Use α = 5%

iii. Find the p-value of the test in ii. above.

Question 4:

a. A television manufacturer claims that not more than 10% of its television sets will need any repair during their first 2 years of operation. To test this claim, a random sample of 100 TV sets are monitored for the first two years of their operation and 14 are found to need repair. At the 5% level of significance, test the manufacturers claim. [Use H_o : p = 0.1  H_A : p > 0.1]

b. A new employee at a large firm was interested in determining whether there was a relationship between the experience of the employees and the salaries. He performed a simple linear regression to help him understand this relationship. The results of this regression are presented in the output which follows.

Use the output provided to answer the following questions.

i. Determine the regression equation to predict salary from years of experience.

ii. Interpret the slope coefficient.

iii. From the scatterplot, it appears that salary is linearly related to years of experience. Test this relationship at a 5% level of significance.

iv. With reference to the plots provided, does it appear that the linear model fitted in Excel is appropriate?

PART B:

1. You are looking at the sales figures for 35 companies. The variable is

A. quantitative and ordinal.
B. qualitative and ordinal.
C. quantitative and nominal.
D. qualitative and nominal.
E. quantitative and ratio.

2. We have a set of data with 200 data values. The minimum value is 2.5 and the maximum value is 80. Which set of class intervals should be used to prepare the frequency distribution.

A.

> 0 up to and including 5
> 5 up to and including 10
> 10 up to and including 15
> 15 up to and including 20
> 20 up to and including 25
> 25 up to and including 30
> 30 up to and including 35
> 35 up to and including 40
> 40 up to and including 45
> 45 up to and including 50
> 50 up to and including 55
> 55 up to and including 60
> 60 up to and including 65
> 65 up to and including 70
> 70 up to and including 75
> 75 up to and including 80

B.

0 to 10
10 to 20
20 to 30
30 to 40
40 to 50
50 to 60
60 to 70
70 to 80

C.

> 2.5 up to and including 12.5
> 12.5 up to and including 22.5
> 22.5 up to and including 32.5
> 32.5 up to and including 42.5
> 42.5 up to and including 52.5
> 52.5 up to and including 62.5
> 62.5 up to and including 72.5
> 72.5 up to and including 82.5

D.

> 0 up to and including 10
> 10 up to and including 20
> 20 up to and including 30
> 30 up to and including 40
> 40 up to and including 50
> 50 up to and including 60
> 60 up to and including 70
>70 up to and including 80

E.

> 0 up to and including 20
> 20 up to and including 40
> 40 up to and including 60
> 60 up to and including 80

3. All 18 people in a department have just received across-the-board pay rises of 4%. What has happened to the standard deviation of these salaries?

A. The standard deviation has stayed the same.
B. The standard deviation has increased by 4%.
C. The standard deviation has increased by 2%
D. The standard deviation has decreased by 4%
E. We are unable to determine this, without the actual salaries.

4. Which type of graphical display would allow us to determine a specific percentile most easily?

A. A cumulative relative frequency polygon (ogive).
B. A cumulative relative frequency histogram.
C. A boxplot.
D. A relative frequency polygon.
E. A relative frequency histogram.

5. The histogram following shows the length of hospital stay (in days) for a sample of patients.

The distribution shape is best described as

A. positively skewed.
B. negatively skewed.
C. approximately normally distributed.
D. unimodal.
E. bimodal.

6. If a box of camera film has 10 rolls in it and 3 have already been used. What is the probability of selecting 2 rolls and finding both are unused?

A. 0.067
B. 0.21
C. 0.467
D. 0.49
E. 0.933

7. Given that Z is a standard normal random variable, find P(Z < 2.3)

A. 0.9893
B. 0.9890
C. 0.4893
D. 0.0107
E. 0.4890

Use the following information to answer questions 8. and 9.
The owner of the local service station notices that on average, 10 cars arrives every ten minutes. If we assume that cars arrive randomly and independently,

8. find the probability that exactly 3 cars arrive in the next ten minutes.

A. 0.172
B. 0.117
C. 0.010
D. 0.003
E. 0.007

9. find the probability that fewer than 5 cars arrive in the next five minutes.

A. 0.067
B. 0.038
C. 0.616
D. 0.176
E. 0.440

10. An automatic transmission factory, which produces, on average, 400 transmissions daily, has had some problems with quality. The manager decides to gather information from tomorrow's production for careful evaluation. Which of the following sampling methods would provide the best estimate of the proportion of defective transmissions being produced?

A. The first five transmissions produced.
B. The 18 transmissions that are sitting outside the plant because they never worked.
C. Every 200th transmission produced.
D. A random sampling taken at the end of the day from the day's production.
E. All obviously defective transmissions together with a random sampling of the apparently non-defective ones.

11. Which of the following statements about normal distributions is false?

A. Normal distributions are bell shaped.
B. Normal distributions always have a mean of zero and standard deviation of 1.
C. In a normal distribution, the .
D. A normal distribution is symmetrical.
E. About 68 % of observations lie within 1 standard deviation of the mean.

12. If the level of significance is changed from 5% to 10%, the probability of rejecting a null hypothesis which is actually true becomes

A. lower.
B. higher.
C. remains the same.
D. depends on whether it is a one or two tailed test.
E. none of the above.

13. In a packet of 50 seeds, two did not germinate. Estimate a 95% confidence
interval for the population proportion of seeds that will not germinate.

A. 0.04 ± 1.96 √[(0.04x0.96)/50]
B. 0.04 ± 1.645 √[(0.04x0.96)/50]
C. 0.96 ± 1.96 √[(0.96x0.04)/50]
D. 0.96 ± 1.645 √[(0.96x0.04)/50]
E. none of the above since both and are not greater than 5.

Use the following information to answer questions 14 and 15.

If the null and alternative hypotheses are

H_o : μ = 100

H_A : μ > 100

14. The appropriate test would be a(n)

A. lower tailed test.
B. two tailed test.
C. upper tailed test.
D. upper tailed test containing only half the level of significance.
E. lower tailed test containing only half the level of significance.

15. If x‾ was found to be equal to 102.3, given that σ² = 25 and n = 36, the appropriate test statistic would be

A. t = (102.3 - 100)/(5/√36)
B. z = (102.3 - 100)/(5/√36)
C. t = (102.3 - 100)/5
D. z = (102.3 - 100)/5
E. z = (102.3 - 100)/(25/√36)

16. The p-value for a certain hypothesis test was 0.15. The level of significance
used for this test was 0.05. With this information we should

A. reject H_o.
B. do not reject H_o.
C. accept H_A.
D. do not reject H_A.
E. none of the above.

17. The residuals formed when a regression line is fitted to a data set should ideally

A. be normally distributed.
B. have an expected value of zero.
C. have a variance which is independent of the value of the independent variable.
D. be independent from each other.
E. possess all the characteristics of A., B., C. and D.

Use the following information to answer questions 18., 19. and 20.

The output following shows the regression statistics for the simple linear regression between the earnings per share and the closing stock price of selected biotechnical firms with large market capitalisation.

18. The correlation between the earnings per share and the closing stock price is

A. 0.179
B. -0.179
C. 0.423
D. -0.423
E. unable to be determined from the information provided.

19. The 99% confidence interval estimate of the y-intercept (β_o) is

A. -$1.14 to -$0.14
B. -$0.01 to $0.06
C. -$1.01 to -$0.28
D. -$0.00 to $0.05
E. unable to be determined from the information given

20. If we wanted to test for a significant correlation (α = 0.01) between the earnings per share and the closing stock price, the critical t value would be

A. t_0.01,19
B. t_0.005,18
C. t_0.01,17
D. t_0.01,18
E. t_0.005,19