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Statistics

STAT-2903

Bob Bector

Winter

Description

STAT-1201 Introduction to Statistical Analysis, SAMPLE Final Exam
Special Instructions:
1. FORMULAE ARE SECTION SPECIFIC.
YOUR INSTRUCTOR WILL PROVIDE YOU WITH THE FORMULAE SHEET .
2. Necessary statistical tables are provided.
3. Show all your work in the examination booklet provided.
4. Only non-programmed hand calculators may be used.
5. Whenever necessary state H a0d H cle1rly and draw appropriate conclusions.
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PART A: 70 MARKS
– Answer any 10 of the following 12 questions.
– Each is worth 7 marks
1. The change in temperature between the warmest and coolest parts of the day measures
the sun’s thermal heating of the earth (called Diurnal Temperature Variation).
Temperature changes (in F) for ten days are recorded as follows:
11.3 10.3 11.6 14.5 15.2 13.9 13.6 11.0 16.0 16.0
(a) Determine the median, and also the ﬁrst and third quartiles.
(b) Determine the sample mean and the sample standard deviation.
(c) Determine the percentage of observations that falls within 2 standard
deviations of the mean.
2. The probability that one drug-resistant bacterium will be killed by the application of a
ﬁrst-line drug A is 0.6, and the probability that the bacterium will be killed by a more
costly second-line drug B is 0.7; the probability that both drugs will kill the bacterium
(A ∩ B) is 0.50.
(a) What is the probability that the bacterium is killed by at least one of the
drugs applied?
(b) What is the probability that the bacterium is not killed by either of the two
drugs applied?
(c) Are events A and B mutually exclusive? Explain.
(d) Are events A and B independent? Explain.
/...to page two STAT-53.1201/6 Page 2 of 5
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3. (a) A hockey goalie has a 0.89 chance per shot of preventing a goal. What is the
probability that, out of ten shots taken, exactly one goal occurs.
(b) For a recent period of 100 years, the average number per year of major
earthquakes (at least 6.0 on the Richter scale) was 0.93. Assuming that the
Poisson distribution is a suitable model, ﬁnd the probability that no
earthquakes occur in a year.
(c) In an experiment for cross-breeding, there are eight tropical ﬁsh of which ﬁve
are female. If four ﬁsh are selected at random without replacement, ﬁnd the
probability that exactly two are female.
4. The average of sodium content in a certain brand of low-salt microwave frozen dinners is
660 mg, and the standard deviation is 35 mg. Assume the variable is normally
distributed.
(a) If a single dinner is selected, ﬁnd the probability that the sodium content will
be more than 670 mg.
(b) If a sample of 10 dinners is selected, ﬁnd the probability that the mean of the
sample will be larger than 670 mg.
(c) Why is the probability for part (a) greater than that for part (b)?
5. Given that the heights of all female college basketball players have a normal distribution
with a mean of 68 inches and a standard deviation of 2 inches, you extract a random
sample of 16 female college basketball players.
(a) Find the probability that the mean height of the sample will be more than
68.8 inches.
(b) Determine the 97 th percentile of the distribution of the sample mean.
6. (a) A survey of 1275 Canadians indicated that 1224 prefer buying products that
can be recycled. Find a 95% conﬁdence interval for the true population
proportion.
(b) A survey of 1100 hospital admissions reports that the average length of stay
for seniors aged 65 and over who are hospitalized for falls is 13 days. Find a
point estimate of the population mean. Find the 98% conﬁdence interval of
the true mean. Assume the population standard deviation was 1.3 days.
7. (a) The standard deviation of the viscosity of a brand of engine oil is 0.02. How
large a sample would be needed for a 95% conﬁdence interval to be within
0.005 units of the population mean?
(b) A maker of diet meals claims that the average calorie content of its meals is
800. A researcher tested 12 meals and found that the average number of
calories was 873 with a standard deviation of 25. Does the evidence support
the claim at α = 0.05? Assume normality of the population.
/...to page three STAT-53.1201/6 Page 3 of 5
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8. The distribution of diastolic blood pressures for the population of female diabetics
between the ages of 30 and 34 has an unknown mean µ and standard
deviation σ = 9.1 mm Hg. It may be useful to physicians to know whether the mean
diastolic blood pressure of this group is equal to the mean diastolic blood pressure of the
general population of females in this age group, 74.4 mm Hg.
(a) What is the null hypothesis of the appropriate test?
(b) What is the alternative hypothesis?
(c) A sample of ten diabetic women is selected; their mean diastolic blood
pressure isx = 84 mm Hg. Using this information, conduct a test at the
α = 0.05 level of signiﬁcance.
(d) What conclusion do you draw from the results of the test?
(e) Would your conclusion have been diﬀerent if you had chosen α = 0.01 instead
of α = 0.05?
9. A survey was conducted to compare the proportions of males and females who favor
government assistance for child care. It was found that among 64 males interviewed, 40
favoured assistance, and among 100 females, 70 favoured assistance. Are the true
proportions among males and females in the population who favour government
assistance for child care signiﬁcantly diﬀ

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