# MCQs, Confidence Interval, Probability & Hypothesis Testing

Week 8:

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1. (TCO 9) What is the feasible range for r, the correlation coefficient? (Points: 6)

0 to 1

-0.5 to 0.5

-1 to 1

-1 to 0

2. (TCO 5) The Canadian Services office did a survey of 150 travelers in which they asked if the traveler's first language was French or English. Another question asked was whether the traveler was Canadian born. The results follow.

If a traveler is selected at random (from this group of 150 travelers), find the probability that

P(The traveler is a Canadian.) (Points: 6)

7/15

8/15

13/30

4/17

3. (TCO 5) The Canadian Services office did a survey of 150 travelers in which they asked if the traveler's first language was French or English. Another question asked was whether the traveler was Canadian born. The results follow.

If a traveler is selected at random (from this group of 150 travelers), find the probability that

P(The traveler is not Canadian and speaks French as the first language.) (Points: 6)

20/85

20/70

0.135

20/150

4. (TCO 5) The Canadian Services office did a survey of 150 travelers in which they asked if the traveler's first language was French or English. Another question asked was whether the traveler was Canadian born. The results follow.

If a traveler is selected at random (from this group of 150 travelers), find the probability that

P (The traveler speaks French as a first language given he is a Canadian.) (Points: 6)

65/150

0.800

65/80

65/85

5. (TCO 2) In a study done by the National Health Foundation, it was determined that the mean number of headaches for women is 14 per year with a standard deviation of 2.5.

How many standard deviations is 16.50 from the mean? (Points: 6)

1.25

1.00

0.75

0.50

6. (TCO 6) Find the following probability involving the Standard Normal Distribution. What is P(z < 0.25)? (Points: 6)

0.4013

0.9938

0.8944

0.5987

7. (TCO 8) Suppose you are performing a hypothesis test on a claim about a population proportion. Using an alpha = 0.01 and n = 100, what is the rejection region if the alternate hypothesis is Ha: p > 0.75? (Points: 6)

Reject Ho if z > 1.28

Reject Ho if z > 1.64

Reject Ho if z < -2.33

reject Ho if z > 2.33

8. (TCO 8) Suppose you are performing a hypothesis test on a claim about a population proportion. Using an alpha = 0.05 and n = 90, what two critical values determine the rejection region if the null hypothesis is: Ho: p = 0.35? (Points: 5)

1.28, -1.28

1.96, -1.96

2.33, -2.33

none of these

9. (TCO 2) If the standard deviation of some data is 36, what is the variance? (Points: 5)

6

72

1296

720

10. (TCO 1) Determine the minimum required sample size if you want to be 95% confident that the sample mean is within 3 units of the population mean given sigma = 7.8. Assume the population is normally distributed. (Points: 5)

6

26

13

52

11. (TCO 3) The stem and leaf plot for the following data is displayed below: {70, 78, 76, 55, 43, 56, 32, 67, 68, 71, 75, 67, 60, 62, 58, 75, 21}

Stem and Leaf Plot:

2 | 1

3 | 2

4 | 3

5 | 5 6 8

6 | 0 2 7 7 8

7 | 0 1 5 5 6 8

What is the shape of the data distribution? (Points: 5)

uniform

skewed left

skewed right

symmetric

12. (TCO 4) The random variable X represents the annual salaries in dollars of a group of teachers. Find the expected value E(X).

X = {$30,000, $40,000, $50,000}

P(30,000) = 0.6; P(40,000) = 0.3; P(50,000) = 0.1 (Points: 5)

$18,000

$35,000

$30,000

$22,000

13. (TCO 6) Scores on an exam for entering a private school are normally distributed, with a mean of 72 and a standard deviation of 6. To be eligible to enter, a person must score in the top 5%. What is the lowest score you can earn and still be eligible to enter? (Points: 5)

82

72

80

78

14. (TCO 5) A shipment of 50 television sets contains 3 defective units. How many ways can a vending company buy three of these units and receive no defective units? (Points: 5)

50

10, 210

16,215

12, 324

15. (TCO 6) The time required to process a ton of sugar cane in a plant in Central America in a recent year was normally distributed with a mean 5 days and a standard deviation of 0.5 days (i.e., 12 hours). What is the probability that it will take more than 6 days to process a ton of sugar cane? (Points: 5)

0.9772

0.0228

0.8413

0.1587

16. (TCO 10) The earnings per share (in dollars) for McDonald's Corporation are given by the equation y-hat = 0.668 + 0.046a - 0.015b where 'a' represents total revenue (in billions of dollars) and 'b' represents total net worth (in billions of dollars). Predict the earnings per share when total revenue is $10 billion and net worth is $5 billion. (Points: 5)

1.053

0.778

0.061

0.984

17. (TCO 9) The estimated value for the correlation coefficient for this graph might be

(Points: 3)

-0.50

0.50

1.00

-0.85

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1. (TCO 11) A restaurant claims that its speed of service time is less than 18 minutes. A random selection of 36 service times was collected, and their mean was calculated to be 17.1 minutes. Their standard deviation is 3.1 minutes. Is there enough evidence to support the claim at alpha = 0.08? Perform an appropriate hypothesis test, showing each important step. (Note: 1st Step: Write Ho and Ha; 2nd Step: Determine Rejection Region; etc.) (Points: 20)

2. (TCO 2) The heights of 8 fourth graders are listed in inches: {50, 54, 55, 52, 59, 54, 54, 53}. Find the mean, median, mode, variance, and range. Also, do you think this sample might have come from a normal population? Why or why not? (Points: 20)

3. (TCO 5) A hospital is hoping to introduce a Fast Care Unit. The hospital claims that after the initial run, 78% of the patients were pleased with the service. We ask 10 randomly selected patients whether or not they are pleased with the service.

a) Is this a binomial experiment? Explain how you know.

b) Use the correct formula to find the probability that, out of 10 patients, exactly 7 are pleased with the service. Show your calculations.

(Points: 20)

4. (TCO 6) The average monthly gasoline (gallon) purchase for a family with 2 cars is 62 gallons. This statistic has a normal distribution with a standard deviation = 6 gallons. A family is chosen at random.

a) Find the probability that the family's monthly gasoline (gallon) purchases will be between 47 and 67 gallons.

b) Find the probability that the family's monthly gasoline (gallon) purchases will be less than 67 gallons.

c) What is the probability that the family's monthly gasoline (gallon) purchases will be more than 47 gallons?

(Points: 20)

5. (TCO 7) A marketing firm wants to estimate the average amount spent by patients at the hospital pharmacy. For a sample of 140 randomly selected patients, the mean amount spent was $86.50 and the standard deviation was $11.45.

a. Find a 95% confidence interval for the mean amount spent by patients at the pharmacy. Show your calculations.

b. Interpret this confidence interval and write a sentence that explains it.

(Points: 20)

6. (TCO 7) A drug manufacturer wants to estimate the mean heart rate for patients with a certain heart condition. Because the condition is rare, the manufacturer can only find 19 people with the condition currently untreated. From this small sample, the mean heart rate is 93 beats per minute with a standard deviation of 7.

a. Find a 98% confidence interval for the true mean heart rate of all people with this untreated condition. Show your calculations.

b. Interpret this confidence interval and write a sentence that explains it.

(Points: 20)

7. (TCO 8) For the following statement, write the null hypothesis and the alternative hypothesis. Then, label the one that is the claim being made.

A bus drivers' union claims that the mean age of a bus driver in Chicago is 55.3 years. (Points: 20)

8. (TCO 8) A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1050 hours. A homeowner selects 40 bulbs and finds the mean lifetime to be 1030 hours with a standard deviation of 80 hours. Test the manufacturer's claim. Use alpha = 0.06. (Points: 20)

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#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis, confidence interval, normal probability, binomial probability and descriptive statistics. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.