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UNIVERSITY OF

KWAZULU-NATAL

SCHOOL OF STATISTICS & ACTUARIAL SCIENCE

EXAMINATIONS

9 NOVEMBER 2006

COURSE AND CODE

BASIC STATISTICS (STAT101)

_________________________________________________________________________DURATION: 2hours

TOTAL MARKS: 80

INTERNAL EXAMINER: Miss K Leask

EXTERNAL EXAMINER: Dr P Ndlovu, UKZN (PMB)

THIS EXAM PAPER CONSISTS OF A TOTAL OF 10 PAGES INCLUDING THIS

ONE. PLEASE SEE THAT YOU HAVE THEM ALL.

SECTION A - MULTIPLE CHOICE

45 MARKS

INSTRUCTIONS:

1. Answer this section on the MCQ answer sheet using an HB pencil only.

2. Please fill in your name and studentnumber on the MCQ sheet BEFORE

STARTING THE EXAMINATION.

3. There is no penalty for incorrect answers on this section, so do not leave any

question out. This section counts for 45 marks.

4. A formula sheet is provided on page 8.

5. Statistical tables appear on pages 9 and 10.

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UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS 9 NOVEMBER 2006

BASIC STATISTICS (STAT101) 2

THE NEXT FIVE QUESTIONS REFER TO THE FOLLOWING PROBLEM

SETTING:

The body temperatures (in degrees Fahrenheit) of 10 patients hospitalized with meningitis

were recorded as follows:

104.0 104.8 101.6 105.0 103.8 100.8 104.2 100.2 102.4 101.4

1. The variable body temperature isa. Discrete, quantitative

b. Discrete, qualitativec. Continuous, quantitatived. Continuous, qualitativee. None of the above

2. The sample mean isa.

102.28b. 102.82

c. 103.41d. 102.69e. None of the above

3. The sample median isa. 102.4

b. 103.8c. 103.1d. 103.0e. None of the above

4. If the observation 104.8 is omitted from the sample the median isa. the same as the original sample


5. The sample range isa. 4.0


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THE NEXT FOUR QUESTIONS REFER TO THE FOLLOWING PROBLEM

SETTING:

90 dog owners were asked how much they have spent in the last year for their dogs health

care, and whether their dogs were purebred or mixed breeds. The following table contains

the distribution of the amount spent by type of dog.

Type of dog

Amount spent Purebred Mixed breed

Less than R1000 0.211 0.233

R1000 or more 0.389 0.167

6. The probability that R1000 or more was spent on a randomly selected dogs healthcare last year is

a. 0.389b. 0.167c. 0.065d. 0.556e. None of the above

7. Given that a randomly selected dog owner spent less than R1000, the probabilitythat the dog was a mixed breed is

a. 0.444b. 0.4c. 1.11d. 0.233e. 0.525

8. The probability that a randomly selected owner spent R1000 or more on health careand the dog being a mixed breed is


9. The events spending R1000 or more on health care and having a mixed breeddog are

a. Independentb. Dependentc. Complementary eventsd. Conditional eventse. None of the above

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10.A surgical technique is performed on eight patients and it has been reported thatthere is an 80% chance of success. The probability that the procedure is successful

for exactly four patients is


11.A newspaper finds that the mean number of typographical errors per page is 5. Theprobability that more than five typographical errors will be found on a page is

a. 0.616b. 0.176c. 0.440d. 0.238e.

0.384

THE NEXT TWO QUESTIONS REFER TO THE FOLLOWING PROBLEM

SETTING:A manufacturer claims that the watt usage of its 17-inch flat panel monitors is less than that

of its leading competitor. He wishes to determine if there is enough evidence to support his

claim and decides to use a significance level of 0.10. Note that 1 represents the mean of

the 17-inch flat panel monitors and 2 represents the mean of the leading competitor.

12.The null and alternative hypotheses for this situation are:a. H0: 1 2, H1: 1 > 2

b. H0: 1 2, H1: 1 < 2c. H0: 1 2, H1: 1 = 2d. H0: 1 > 2, H1: 1 = 2e. H0: 1 = 2, H1: 1 2

The MINITAB output for this test is given below:

Two-Sample T-Test and CI

Sample N Mean StDev SE Mean

1 12 73.00 2.40 0.69

2 15 74.00 3.20 0.83

Estimate for difference: -1.00000

T-Test of difference = 0 (vs not =): T-Value = -0.90 P-Value = 0.378 DF = 25

Both use Pooled StDev = 2.8756

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13.We therefore conclude that:a. 1 < 2, at the 10% level of significance

b. H0 is rejected at the 1% level of significancec. There is no convincing evidence that 1 < 2, at the 10% level of

significance

d. H0 is rejected at the 5% level of significancee. None of the above

14. A light bulb manufacturer tests the mean life of a certain type of light bulb to see if

he can claim that this mean life is greater than 750 hours. They do not want to

market this light unless there is strong evidence indicating that the mean life is

greater than 750 hours. After testing a sample of bulbs, the manufacturer decides to

market the bulb. Actually, however, the mean life is less than 750 hours. Which

type of error, if any, did the manufacturer commit?

a. This is a Type I error.b. This is a Type II error.c. This is a correct decision.d. Need more information to answer this question

15. Which of the following must be avoided in designing a questionnaire?

a. Dichotomous questions.b. Leading questions.c. Open-ended questions.d. Demographic questions.

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SECTION B WRITTEN SECTION

35 MARKS

THIS SECTION SHOULD BE COMPLETED IN AN ANSWER BOOK.

I. Attempt all questions neatly.II. Please write legibly, unreadable answer may not be marked.

QUESTION 1

The following data represents the amount of time (in minutes) 25 people spend reading thenewspaper in the morning.

7 32 13 9 25 8 22 0 2 18 2 30 7

35 12 15 8 6 5 29 0 11 24 16 15

a) Are there any outliers in this data? (3)b) Construct a box-and-whisker plot for the above data set. (5)c) Comment on the shape of the distribution. (2)

[10]

QUESTION 2

The aptitude test scores of applicants to a university program are normally distributed with

mean = 400 and standard deviation = 100.a. An applicant needs a test score higher than 525 to be admitted into the graduate

program. What proportion of applicants qualifies?(4)

b. Suppose fifty applicants write the test. What is the probability that the average scorefor these applicants exceeds 525? (5)

[9]

QUESTION 3

A medical investigator states that half the elderly people given anaesthetics for operations

suffer from complications. On examining his records he found that 36 such people out of a

random sample of 100 in fact have complications. Construct a 95% confidence interval for

the proportion of elderly people suffering from complications. From the intervalconstructed, does his claim appear to be valid?

[6]

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QUESTION 4

You work for a colleges continuing education department and want to determine whether

the reasons given by workers for continuing their education is related to job type. You

randomly collect the data shown in the contingency table below:

Reason

Type of

Worker

Professional Personal Professional and

personal

Technical 30 36 41

Other 47 25 30

a. State the null and alternative hypotheses for this test. (2)b. Use the MINITAB output given below to answer the following questions:

Chi-Square Test: professional, personal, prof/pers

Expected counts are printed below observed counts

Chi-Square contributions are printed below expected counts

professional personal prof/pers Total

1 30 36 41 107

39.42 31.23 36.35

2.251 0.729 0.595

2 47 25 30 102

37.58 29.77 34.65

2.362 0.764 0.624

Total 77 61 71 209

Chi-Sq = 7.326, DF = 2, P-Value = 0.026

i. Write down the p-value for this test. (1)ii. Using = 0.05, is the null hypothesis rejected? State a suitable conclusion for

this hypothesis test. (2)

[5]

QUESTION 5

A Statistics lecturer wanted to establish an equation for predicting the test score (Y) of aStatistics student from the total amount of time (X) spent by the student studying for the

test. Eight randomly chosen students were asked to record their study times for an

impending Statistics test. After two days the test was given, and the test score (Y) of each

of the eight students was matched with total amount of time (X) the student spent studying

for the test. Here are the descriptive statistics:

117,1869,9519,54638,660 22 ===== xxxyyy

a. Calculate the correlation coefficient for the above data. (3)b. Obtain the simple linear regression line used to predict Y from X. (5)c. Interpret the slope coefficient of the regression line obtained in part (b).

(2)

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