STK110 Preparation sheet: TUT 8 2023
Question 1
a. It is reasonable to assume that the age distribution of Comrades athletes that finish a race is normally
distributed with standard deviation of 9 years. If the average age of a random sample of 25 Comrades athletes
that finished a race is 35, calculate a 99% confidence interval for the population mean age of Comrades
athletes that finish a race.
b. The school psychologist is currently busy studying stress during exam time. She has developed a
questionnaire that she believes measures stress. A score above 80 indicates stress at a dangerous level. A
random sample of 16 senior learners revealed an average stress level of 89.29. You may assume that stress
levels are normally distributed with a standard deviation of 8. Calculate a 90% confidence interval for the
population mean stress level of senior learners. What can you conclude from this result?
c. Suppose we wish to estimate the mean age at which patients with hypertension is diagnosed. The ages of 12
randomly selected individuals diagnosed with hypertension, were recorded. We assume that age at diagnoses
is approximate normally distributed with known standard deviation of 7.2. Calculate a 95% CI
Data: 32.8 40.0 41.0 42.0 45.5 47.0 48.5 50.0 51.0 52.0 54.0 59.2
Question 2
a. Eight randomly chosen Comrades participants were asked their age (in years), The following data was
observed: 36, 40, 27, 30, 34, 38, 25, and 45.
Find a 98% interval estimate of the average age of a Comrades participant.
b. The school psychologist is currently busy studying stress during exam time. She has developed a
questionnaire that she believes measures stress.
A score above 80 indicates stress at a dangerous level. A random sample of 9 senior learners revealed the
following data:
85 75 88 90 79 75 84 87 94
Calculate a 80% confidence interval for the population mean stress level of senior learners. What can you
conclude from this result?
c. Eight bolts of cloth, randomly selected from a factory production line at a textile factory, are each tested for
their tearing strength (the amount of force required to tear the cloth, measured in kilograms). The results are:
4.9 4.7 5.1 5.4 4.7 5.2 4.8 5.1
Calculate a 95% confidence interval for the population mean tearing strength.
Question 3
a. The school has a monthly newsletter which publishes important events, news and competitions. To justify the
time and effort to publish the newsletter, a certain percentage of the learners has to read the newsletter. In a
random sample of 40 learners it is found that 27 read the newsletter regularly. What is the 95% interval
estimate of the proportion of the population of learners that read the newsletter?
b. An entomologist samples a field for egg masses of a harmful insect by placing a metre-square frame at
random locations and carefully examining the ground within the frame. A simple random sample of 75
locations selected from a farmer’s pastureland found egg masses in 13 locations. Find a 90% confidence
interval estimate of the proportion of all possible locations that are infested.
c. In the winter of 2015, 15% of all paediatric outpatient visits at a particular clinic were due to a single strain of
flu. Suppose that flu shots were given to a random sample of 125 paediatric patients in the fall of 2016. Of
those patients 15 were seen in the winter of 2016 for flu. Calculate a 96% confidence interval for the
population proportion of paediatric patients that will get the flu. What can you conclude?
Suggested solutions:
Question 1 Question 2 Question 3
a. (30.365, 39.635) a. (27.1875, 41.5625) a. (0.5298, 0.8202)
b. (86, 92.58) b. (81.0359, 87.1863) b. (0.1014, 0.2452)
c. (42.8429, 50.9938) c. (4.7758, 5.1992) c. (0.0604, 0.1796)
Question 1
a. It is reasonable to assume that the age distribution of Comrades athletes that finish a race is normally
distributed with standard deviation of 9 years. If the average age of a random sample of 25 Comrades athletes
that finished a race is 35, calculate a 99% confidence interval for the population mean age of Comrades
athletes that finish a race.
b. The school psychologist is currently busy studying stress during exam time. She has developed a
questionnaire that she believes measures stress. A score above 80 indicates stress at a dangerous level. A
random sample of 16 senior learners revealed an average stress level of 89.29. You may assume that stress
levels are normally distributed with a standard deviation of 8. Calculate a 90% confidence interval for the
population mean stress level of senior learners. What can you conclude from this result?
c. Suppose we wish to estimate the mean age at which patients with hypertension is diagnosed. The ages of 12
randomly selected individuals diagnosed with hypertension, were recorded. We assume that age at diagnoses
is approximate normally distributed with known standard deviation of 7.2. Calculate a 95% CI
Data: 32.8 40.0 41.0 42.0 45.5 47.0 48.5 50.0 51.0 52.0 54.0 59.2
Question 2
a. Eight randomly chosen Comrades participants were asked their age (in years), The following data was
observed: 36, 40, 27, 30, 34, 38, 25, and 45.
Find a 98% interval estimate of the average age of a Comrades participant.
b. The school psychologist is currently busy studying stress during exam time. She has developed a
questionnaire that she believes measures stress.
A score above 80 indicates stress at a dangerous level. A random sample of 9 senior learners revealed the
following data:
85 75 88 90 79 75 84 87 94
Calculate a 80% confidence interval for the population mean stress level of senior learners. What can you
conclude from this result?
c. Eight bolts of cloth, randomly selected from a factory production line at a textile factory, are each tested for
their tearing strength (the amount of force required to tear the cloth, measured in kilograms). The results are:
4.9 4.7 5.1 5.4 4.7 5.2 4.8 5.1
Calculate a 95% confidence interval for the population mean tearing strength.
Question 3
a. The school has a monthly newsletter which publishes important events, news and competitions. To justify the
time and effort to publish the newsletter, a certain percentage of the learners has to read the newsletter. In a
random sample of 40 learners it is found that 27 read the newsletter regularly. What is the 95% interval
estimate of the proportion of the population of learners that read the newsletter?
b. An entomologist samples a field for egg masses of a harmful insect by placing a metre-square frame at
random locations and carefully examining the ground within the frame. A simple random sample of 75
locations selected from a farmer’s pastureland found egg masses in 13 locations. Find a 90% confidence
interval estimate of the proportion of all possible locations that are infested.
c. In the winter of 2015, 15% of all paediatric outpatient visits at a particular clinic were due to a single strain of
flu. Suppose that flu shots were given to a random sample of 125 paediatric patients in the fall of 2016. Of
those patients 15 were seen in the winter of 2016 for flu. Calculate a 96% confidence interval for the
population proportion of paediatric patients that will get the flu. What can you conclude?
Suggested solutions:
Question 1 Question 2 Question 3
a. (30.365, 39.635) a. (27.1875, 41.5625) a. (0.5298, 0.8202)
b. (86, 92.58) b. (81.0359, 87.1863) b. (0.1014, 0.2452)
c. (42.8429, 50.9938) c. (4.7758, 5.1992) c. (0.0604, 0.1796)
