STK110 TUT 8 on Chapter 8 MEMORANDUM
Question 1 a) It is reasonable to assume b) The school psychologist is currently busy c) Suppose we wish to estimate the
that the age distribution of studying stress during exam time. She has mean age at which patients with
Interval estimation: Comrades athletes that finish developed a questionnaire that she believes hypertension is diagnosed.
Population mean, 𝝈 known a race is normal distributed measures stress. 12 Randomly selected individuals
with standard deviation of 9 A score above 80 indicates stress at a dangerous with diagnosed hypertension ages
𝜎 years. If the average age of a level. A random sample of 16 senior learners were recorded. We assume that age
𝑥̅ 𝑧 random sample of 25 revealed an average stress level of 89.29. at diagnoses is approximately
√𝑛 Comrades athletes that normally distributed with known
finished a race is 35, You may assume that stress levels are normally standard deviation of 7.2. Calculate
calculate a 99% confidence distributed with a standard deviation of 8. a 95% confidence interval
interval for the population Data: 32.8 40.0 41.0 42.0 45.5 47.0
mean age of Comrades Calculate a 90% confidence interval for the 48.5 50.0 51.0 52.0 54.0 59.2
athletes that finish a race. population mean stress level of senior learners.
What can you conclude from this result?
Sample average 35 89.29 46.9167
Sample size 25 16 12
Population standard deviation 9 8 7.2
Confidence coefficient 0.99 0.90 0.95
Confidence interval 𝜎 𝜎 𝜎
𝑥̅ 𝑧 𝑥̅ 𝑧 𝑥̅ 𝑧
√𝑛 √𝑛 √𝑛
9 8 7.2
35 2.575 89.29 1.645 46.9167 1.96
5 4 √12
(30.365, 39.635) (86, 92.58) = 46.9167 4.0738
(42.8429, 50.9938)
Question 1 a) It is reasonable to assume b) The school psychologist is currently busy c) Suppose we wish to estimate the
that the age distribution of studying stress during exam time. She has mean age at which patients with
Interval estimation: Comrades athletes that finish developed a questionnaire that she believes hypertension is diagnosed.
Population mean, 𝝈 known a race is normal distributed measures stress. 12 Randomly selected individuals
with standard deviation of 9 A score above 80 indicates stress at a dangerous with diagnosed hypertension ages
𝜎 years. If the average age of a level. A random sample of 16 senior learners were recorded. We assume that age
𝑥̅ 𝑧 random sample of 25 revealed an average stress level of 89.29. at diagnoses is approximately
√𝑛 Comrades athletes that normally distributed with known
finished a race is 35, You may assume that stress levels are normally standard deviation of 7.2. Calculate
calculate a 99% confidence distributed with a standard deviation of 8. a 95% confidence interval
interval for the population Data: 32.8 40.0 41.0 42.0 45.5 47.0
mean age of Comrades Calculate a 90% confidence interval for the 48.5 50.0 51.0 52.0 54.0 59.2
athletes that finish a race. population mean stress level of senior learners.
What can you conclude from this result?
Sample average 35 89.29 46.9167
Sample size 25 16 12
Population standard deviation 9 8 7.2
Confidence coefficient 0.99 0.90 0.95
Confidence interval 𝜎 𝜎 𝜎
𝑥̅ 𝑧 𝑥̅ 𝑧 𝑥̅ 𝑧
√𝑛 √𝑛 √𝑛
9 8 7.2
35 2.575 89.29 1.645 46.9167 1.96
5 4 √12
(30.365, 39.635) (86, 92.58) = 46.9167 4.0738
(42.8429, 50.9938)
