Q: A micro-brewery's pint glasses are filled with a normal distribution, mean $$471 mL$$, standard deviation $$1.5 mL. $$What is the 90th percentile of the amount filled?

$$471 + 1.2816 \times 1.5 = 472.92 mL$$

Q: A poll of 243 Calgarians found 85 would vote to support the Olympics bid. What is the margin of error for this poll at a 95% confidence level?

$$2 \times \sqrt{\frac{0.3498 \times 0.6502}{243}} \approx 0.061$$

Question 1

A political pollster surveys 500 subscribers of Alberta Views magazine to estimate the proportion of Canadians supporting new anti-terrorism legislation. What is the main sampling problem in this scenario?

Accepted Answer

Sampling bias due to non-representative sample

Question 2

In a population with 52% males and 48% females, 20% are Internet addicts, and 13% are both male and Internet addicts. What is the probability that a randomly chosen person is a woman and not an Internet addict?

Accepted Answer

$$0.35$$

Question 3

A study divides Grade Two boys into two groups: one watches violent cartoons, the other non-violent. The number of violent actions is recorded. What is the purpose of randomly dividing the boys into groups?

Accepted Answer

To eliminate confounding variables and ensure comparability

Question 4

A diagnostic test for carpal tunnel syndrome has sensitivity $$0.67$$ and specificity $$0.58. If 12$$% of administrative workers have the syndrome, what is the probability that a randomly selected worker will test positive?

Accepted Answer

$$0.2636$$

Question 5

Alberta Health Services reports that the probability a patient seeking medical attention for the flu at an ER is approximately $$0.1577. $$What type of probability is this?

Accepted Answer

Empirical probability

Question 6

Of 4540 women who gave birth before age 25, 65 developed breast cancer. Of 1628 women who gave birth at 25 or older, 31 developed breast cancer. What is the relative risk of developing breast cancer for women who gave birth at 25 or older compared to those who gave birth before 25?

Accepted Answer

$$\frac{31/1628}{65/4540} \approx 1.34$$

Question 7

An airline surveys its customers by randomly selecting one flight per day for a week. Which sampling method is this?

Accepted Answer

Cluster sampling

Question 8

A poll of 243 Calgarians found 85 would vote to support the Calgary 2026 Winter Olympics bid. Is the proportion $$\frac{85}{243} = 0.3498 a $$statistic or a parameter?

Accepted Answer

Statistic, because it is calculated from a sample

Question 9

Given the data: 4, 2, 6, 5, 0, 1, 3, with mean $$\bar{x} = 3$$, what is the variance $$s^2$$?

Accepted Answer

$$4.67$$

Question 10

Suppose the distribution of commuting times in a city is bell-shaped with mean $$\mu = 30$$ minutes and standard deviation $$\sigma = 10$$ minutes. What interval contains approximately 68% of all commuting times?

Accepted Answer

$$[20, 40]$$

Question 11

A sports-card collector judges 50 hockey cards, 5 of which are fake. If the probability of judging a fake card as authentic is 0.75, and the probability of judging an authentic card as fake is 0.10, what is the probability that a randomly chosen card is judged as authentic?

Accepted Answer

$$0.825$$

Question 12

Billy and Ken must independently name which of four tires was flat. What is the probability they give the same answer?

Accepted Answer

$$0.25$$

Question 13

A commuter plane has 22 reservations for 18 seats. Each reservation-holder shows up independently with probability $$0.8. $$What is the expected number of people who show up?

Accepted Answer

$$17.6$$

Question 14

A micro-brewery fills pints with a mean of $$471 mL $$and standard deviation $$1.5 mL. $$What is the probability that a randomly selected pint contains between $$470 mL $$and $$472 mL$$?

Accepted Answer

$$0.495$$

Question 15

A diagnostic test for a disease has sensitivity $$0.67$$ and specificity $$0.58. If a $$person tests positive, what is the probability they actually have the disease? (Prevalence is $$0.12.)$$

Accepted Answer

$$0.307$$

Question 16

Which of the following best describes the difference between response bias and non-response bias?

Accepted Answer

Response bias occurs when respondents give inaccurate answers; non-response bias occurs when certain groups are underrepresented because they do not respond.

Question 17

If the standard deviation of a data set is $$s = 2.16$$, what is the variance $$s^2$$?

Accepted Answer

$$4.67$$

Question 18

A micro-brewery's pint glasses are filled with a normal distribution, mean $$471 mL$$, standard deviation $$1.5 mL. $$What is the 90th percentile of the amount filled?

Accepted Answer

$$471 + 1.2816 	imes 1.5 = 472.92 mL$$

Question 19

A poll of 243 Calgarians found 85 would vote to support the Olympics bid. What is the margin of error for this poll at a 95% confidence level?

Accepted Answer

$$2 	imes \sqrt{\frac{0.3498 	imes 0.6502}{243}} \approx 0.061$$

Statistics 205 Midterm Exam #1 Review – Step-by-Step Guidance

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