# Multiple choice questions on Probability & Hypothesis

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Please see attached file. Answers are given in green colour.

Questions 4,10,23 of Section 3 are incomplete.

Answers are Given in Green Color

Question 1 4 points Save

The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The events of increase in house sales and increase in

interest rates in the next 6 months are

A. Statistically independent.

B. Mutually exclusive.

C. Collectively exhaustive.

D. None of the above.

Question 2 4 points Save

A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. What is the probability that a randomly chosen widget produced by the company is defective?

A. 0.078

B. 0.1175

C. 0.156

D. 0.310

Question 3 4 points Save

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that the residents of a household do not own 2 cars and have an income over $25,000 a year is:

A. 0.12

B. 0.18

C. 0.22

D. 0.48

Question 4 4 points Save

If two events are independent, what is the probability that they both occur?

A. 0.

B. 0.50.

C. 1.00.

D. Cannot be determined from the information given.

Question 5 4 points Save

Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.

Referring to TABLE 4-1, what proportion of accidents involved alcohol and a

single vehicle?

A. 25/400 or 6.25%

B. 50/400 or 12.5%

C. 195/400 or 48.75%

D. 245/400 or 61.25%

Question 6 4 points Save

If the outcome of event A is not affected by event B, then events A and B are said to be

A. mutually exclusive.

B. statistically independent.

C collectively exhaustive.

D None of the above.

Question 7 4 points Save

If two events are mutually exclusive and collectively exhaustive, what is

the probability that one or the other occurs?

A. 0.

B. 0.50.

C. 1.00.

D. Cannot be determined from the information given.

Question 8 4 points Save

The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that both house sales and interest rates will increase during the next 6 months is:

A. 0.10

B. 0.185

C. 0.705

D. 0.90

Question 9 4 points Save

For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3770. The value of Z is

A. 0.18

B. 0.81

C. 1.16

D. 1.47

Question 10 4 points Save

The probability that a standard normal random variable, Z, is between 1.00 and 3.00 is 0.1574.

A. True

B False

Question 11 4 points Save

Given that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 47 and 54.

A. 1.246

B. 0.9104

C. 0.5846

D. 0.1564

Question 12 4 points Save

The probability that a standard normal random variable, Z, falls between - 1.50 and 0.81 is 0.7242.

A. True

B. False

Question 13 4 points Save

If a particular batch of data is approximately normally distributed, we would find that approximately

A. 2 of every 3 observations would fall between ± 1 standard deviation

around the mean.

B. 4 of every 5 observations would fall between ± 1.28 standard deviations

around the mean.

C. 19 of every 20 observations would fall between ± 2 standard deviations

around the mean.

D. All the above.

Question 14 4 points Save

A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. Find the age at which payments have ceased for approximately 86% of the plan participants.

A. 72.12

B. 45.26

C. 71.78

D. 62.42

Question 15 4 points Save

If we know that the length of time it takes college students to park their cars follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the point in the distribution in which 75.8% of the college students exceed when trying to find a parking spot in the library parking lot.

A. 2.8 minutes

B. 3.2 minutes

C. 3.4 minutes

D. 4.2 minutes

Question 16 4 points Save

Scientists in the Amazon are trying to find a cure for a deadly disease that is attacking the rain forests there. One of the variables that the scientists have been measuring involves the diameter of the trunk of the trees that have been affected by the disease. Scientists have calculated that the average diameter of the diseased trees is 42 centimeters. They also know that approximately 95% of the diameters fall between 32 and 52 centimeters and almost all of the diseased trees has diameters between 27 and 57 centimeters. When modeling the diameters of diseased trees, which distribution should the scientists use?

A. Poisson distribution

B. Binomial distribution

C. Normal distribution

D. Cumulative distribution

Question 17 4 points Save

The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh between 3 and 5 pounds is _______?

A. 0.1246

B. 0.5546

C. 0.5865

D. 0.6548

Question 18 4 points Save

Suppose that the number of airplanes arriving at an airport per minute is a Poisson process. The average number of airplanes arriving per minute is 3. The probability that exactly 6 planes arrive in the next minute is 0.0504.

A. True

B. False

Question 19 4 points Save

The diameters of 10 randomly selected bolts have a binomial distribution.

A. True

B. False

Question 20 4 points Save

If p remains constant in a binomial distribution, an increase in n will not change the mean.

A. ...

#### Solution Summary

The solution gives answers to multiple choice questions on probability and hypothesis testing.

Multiple choice question from hypothesis testing

In chronological order, state the 5 steps of the standard procedure for hypothesis testing:

1.

2.

3.

4.

5.

Except as directed, check the single best answer.

6. Which of the following could be a valid null hypotheses?

A. μ ≥ 27.9 B. μ < 27.9

7. Which of the following can be rejected by a statistical test?

A. Null hypothesis B. Alternate hypothesis

8. If sample size is 20, which can be used to test a hypothesis about the mean?

A. Z B. t C. Either

9. If sample size is 30, which can be used to test a hypothesis about the mean?

A. Z B. t C. Either

10. The level of significance is the probability of:

A. Rejecting a true null hypothesis B. Accepting a false null hypothesis

11. The probability of Type I error is denoted by which Greek letter?

A. μ B. σ C. α D. β

12. Which kind of test is made for the null hypothesis "μ = 27.9"?

____ A. One-tailed test ____ B. Two-tailed test

13. In a two-tailed test, using Z as test statistic, if the significance level is 0.05, how much probability is in each of the two tails?

A. 1.0% B. 2.5% C. 5.0% D. 7.5%

We sample 100 light bulbs from a manufacturing plant to test the null hypothesis that the mean is 1,200 hours, using a significance level of 0.05. The sample average is 1,150 hours and the standard deviation is 500 hours.

14. What is the null hypothesis?

A. μ = 1,200 hrs B. μ ≠ 1,200 hrs C. μ < 1,200 hrs D. μ > 1,200 hrs

15. What is the alternate hypothesis?

A. μ = 1,200 hrs B. μ ≠ 1,200 hrs C. μ < 1,200 hrs D. μ > 1,200 hrs

16. What is the value of α?

A. 0.010 B. 0.025 C. 0.050 D. Unknown

17. Which statistic can properly be used in this hypothesis test?

A. Z B. t C. Either D. Neither

18. What are the approximate critical values of the test statistic? Indicate two values.

A. -3.0 B. -2.0 C. -1.0 D. +1.0 E. +2.0 F. +3.0

19. What is the value of the test statistic computed from the sample's descriptive statistics?

A. -3.0 B. -2.0 C. -1.0 D. +1.0 E. +2.0 F. +3.0

20. Is the null hypothesis rejected?

A. Yes B. No