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Transcript of STAT101P2_12_2006_Y_P1
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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
b. 102.4c. 103.1d. 101.8e. None of the above
5. The sample range isa. 4.0
b. 3.8c. 4.6d. 4.8e. None of the above
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UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS 9 NOVEMBER 2006
BASIC STATISTICS (STAT101) 3
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
a. 0.4b. 0.556c. 0.956d. 0.167e. None of the above
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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UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS 9 NOVEMBER 2006
BASIC STATISTICS (STAT101) 4
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
a. 0.046b. 0.010c. 0.056d. 0.954e. None of the above
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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UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS 9 NOVEMBER 2006
BASIC STATISTICS (STAT101) 5
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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UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS 9 NOVEMBER 2006
BASIC STATISTICS (STAT101) 6
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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UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS 9 NOVEMBER 2006
BASIC STATISTICS (STAT101) 7
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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