COMM 104 University of Saskatchewan Statistics Hypothesis Testing Exam Practice Questions

1. [20 marks] For each of the following statements, identify whether the statement is true or false, and explain why. Please limit each response to no more than 2 sentences.

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COMM 104 University of Saskatchewan Statistics Hypothesis Testing Exam Practice Questions
1. [20 marks] For each of the following statements, identify whe

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a) The probability that a continuous random variable takes a specific value is 0.

b) Statistical inference is the process of drawing conclusions about unknown statistics by using known parameters.

c) The terms “histogram” and “bar graph” are synonyms.

d) If two events A and B are independent, then there is no overlap between the events on a Venn diagram.

e) The standard deviation of the number 10 is 1.

f) A weighted mean is preferred over an unweighted mean (i.e. a regular sample mean) when each observation has its own unique weight.

g) A z-score is a percentile.

h) Assuming the population is normally distributed, the standard deviation of the sampling distribution of the sample mean will always be less than or equal to the population standard deviation.

i) If the sample size increases, but p stays the same, then the standard deviation of the sampling distribution of the sample proportion decreases.

j) Extreme values should always be excluded from subsequent analysis.

2. [10 marks] A company wants the population mean length of their product to be 5 inches. The company knows the population standard deviation of the length of each product is 0.25 inches, and that the lengths are normally distributed. A quality assurance analyst wants to determine if the manufacturing process results in products that are too short. The analyst gets a sample of 10 units of product, and calculates a sample mean length of 4.75 inches.

Conduct a hypothesis test to determine if the products are too short on average. Show all 5 steps of hypothesis testing. Show all of your work. When you calculate the test statistic, show all of the following: the equation you use, how you plug in, and your final rounded answer (remember, z-scores are always rounded to 2 decimal places). Hint: follow the format shown in Chapter 8.

3. [10 marks] Crave is a large subscription-based internet streaming service for movies

and television shows. Suppose the proportion of Saskatchewanians who have a Crave

subscription is 0.15. Suppose the population of Rosetown, Saskatchewan is 2700 people.

a) What is the probability that between 14% and 17% of people in Rosetown, Saskatchewan have a Crave subscription? Round your standard deviation to 4 decimal places. Hint: look at Example 6 in Chapter 7 of the posted textbook. [7 marks]

Note: In your answer to question 3 part a) please show all of the following:

1) The distribution your random variable follows

2) The probability you are asked to calculate

3) Any tricks you use

4) Your rounded z-score (remember to round your z-score to 2 decimal places)

5) Your final probability

b) What is the probability that more than 18% of people in Rosetown, Saskatchewan have a Crave subscription? Use your standard deviation from part a). [3 marks]

Note: in your answer to question 3 part b), please show all of the following:

1) The probability you are asked to calculate (no need to specify the distribution – it’s the same as in part a))

2) Any tricks you use

3) Your rounded z-score (remember to round your z-score to 2 decimal places)

4) Your final probability

4. [10 marks] Suppose a carnival director in a certain city imposes a patron height limit on an amusement park ride called Terror Mountain, due to safety concerns. Patrons must be at least 4 feet tall to ride Terror Mountain. Suppose patrons’ heights in this city follow a Normal distribution with a mean of 4.4 feet and a standard deviation of 0.8 feet (patrons are mostly children).

Note: make sure to show all of your work in this question. Show the distribution that your random variable follows; state the probability you are asked to calculate; show any tricks you use; show how you standardize, show your rounded z-score (round to 2 decimal places), and state your found value from Table A4.

a) What is the probability that a randomly selected patron would be tall enough to ride Terror Mountain? [5 marks]

b) A group of 3 friends want to ride Terror Mountain. What is the probability that their mean height is greater than 4.5 feet? [5 marks] COMM 104 Web

Final Exam

Winter 2020

Questions

1. [20 marks] For each of the following statements, identify whether the statement is true or

false, and explain why. Please limit each response to no more than 2 sentences.

a) The probability that a continuous random variable takes a specific value is 0.

b) Statistical inference is the process of drawing conclusions about unknown statistics by using

known parameters.

c) The terms “histogram” and “bar graph” are synonyms.

d) If two events A and B are independent, then there is no overlap between the events on a

Venn diagram.

e) The standard deviation of the number 10 is 1.

f) A weighted mean is preferred over an unweighted mean (i.e. a regular sample mean) when

each observation has its own unique weight.

g) A z-score is a percentile.

h) Assuming the population is normally distributed, the standard deviation of the sampling

distribution of the sample mean will always be less than or equal to the population standard

deviation.

i) If the sample size increases, but p stays the same, then the standard deviation of the sampling

distribution of the sample proportion decreases.

j) Extreme values should always be excluded from subsequent analysis.

2. [10 marks] A company wants the population mean length of their product to be 5 inches. The

company knows the population standard deviation of the length of each product is 0.25 inches,

and that the lengths are normally distributed. A quality assurance analyst wants to determine if

the manufacturing process results in products that are too short. The analyst gets a sample of

10 units of product, and calculates a sample mean length of 4.75 inches.

Conduct a hypothesis test to determine if the products are too short on average. Show all 5

steps of hypothesis testing. Show all of your work. When you calculate the test statistic, show

all of the following: the equation you use, how you plug in, and your final rounded answer

(remember, z-scores are always rounded to 2 decimal places). Hint: follow the format shown in

Chapter 8.

COMM 104 Web

Final Exam

Winter 2020

3. [10 marks] Crave is a large subscription-based internet streaming service for movies

and television shows. Suppose the proportion of Saskatchewanians who have a Crave

subscription is 0.15. Suppose the population of Rosetown, Saskatchewan is 2700 people.

a) What is the probability that between 14% and 17% of people in Rosetown, Saskatchewan

have a Crave subscription? Round your standard deviation to 4 decimal places. Hint: look at

Example 6 in Chapter 7 of the posted textbook. [7 marks]

Note: In your answer to question 3 part a) please show all of the following:

1) The distribution your random variable follows

2) The probability you are asked to calculate

3) Any tricks you use

4) Your rounded z-score (remember to round your z-score to 2 decimal places)

5) Your final probability

b) What is the probability that more than 18% of people in Rosetown, Saskatchewan have a

Crave subscription? Use your standard deviation from part a). [3 marks]

Note: in your answer to question 3 part b), please show all of the following:

1) The probability you are asked to calculate (no need to specify the distribution – it’s

the same as in part a))

2) Any tricks you use

3) Your rounded z-score (remember to round your z-score to 2 decimal places)

4) Your final probability

4. [10 marks] Suppose a carnival director in a certain city imposes a patron height limit on an

amusement park ride called Terror Mountain, due to safety concerns. Patrons must be at least

4 feet tall to ride Terror Mountain. Suppose patrons’ heights in this city follow a Normal

distribution with a mean of 4.4 feet and a standard deviation of 0.8 feet (patrons are mostly

children).

Note: make sure to show all of your work in this question. Show the distribution that

your random variable follows; state the probability you are asked to calculate; show any

tricks you use; show how you standardize, show your rounded z-score (round to 2

decimal places), and state your found value from Table A4.

a) What is the probability that a randomly selected patron would be tall enough to ride Terror

Mountain? [5 marks]

b) A group of 3 friends want to ride Terror Mountain. What is the probability that their mean

height is greater than 4.5 feet? [5 marks]

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