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STAT-2903 Study Guide - Final Guide: Poisson Distribution, Richter Magnitude Scale, Blood Pressures


Department
STATISTICS
Course Code
STAT-2903
Professor
Bob Bector
Study Guide
Final

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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 H0and H1clearly 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 Ais 0.6, and the probability that the bacterium will be killed by a more
costly second-line drug Bis 0.7; the probability that both drugs will kill the bacterium
(AB) 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 Aand Bmutually exclusive? Explain.
(d) Are events Aand Bindependent? Explain.
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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 97th 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.
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