1. What is the null hypothesis tested by analysis of variance?

5. What is the difference between “N” and “n”?

8. What kind of skew does the F distribution have?

10. Assume an experiment is conducted with 5 conditions and 6 subjects in each condition.

What are df_{numerator} and df_{denominator}?

Use the following information to answer #61 and #63. Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses.

Null-Hypothesis is H_{0}: μ1 = μ2 = μ3 = μ4 = μ5

Alternate Hypothesis is H_{α}: At least any two of the group means μ1, μ2, …, μ5 are not equal.

61. Find the degrees of freedom (numerator) = *df*(num)

63. Find the F-statistic using an ANOVA table.

69. A researcher wants to know if the mean times (in minutes) that people watch their favorite news station are the same. The table (on right) shows the results of a study. Assume that all distributions are normal, the population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05.

71. Are the mean number of times a month a person eats out the same for whites, blacks, Hispanics and Asians? The table (on right) shows the results of a study. Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05.

77. A grassroots group opposed to a proposed increase in the gas tax claimed that the increase would hurt working-class people the most, since they commute the farthest to work. Suppose that the group randomly surveyed 24 individuals and asked them their daily one-way commuting mileage. The results are as follows (see table). Determine whether or not the variance in mileage driven is statistically the same among the groups. Use a 5% significance level.

81. Is the variance for the amount of money, in dollars, that shoppers spend on Saturdays at the mall the same as the variance for the amount of money that shoppers spend on Sundays at the mall? The table (on right) shows the results of a study.Assume a 10% significance level.

HINT: See Section 13.4 (Test of Two Variances) to find the F-statistic. Assume the null hypothesis is the variances are the same and assume the alternate hypothesis is .

FDIST (F, df1, df2) = FDIST(9.085,4,45) = 0.00001815

1. True or False. Justify for full credit.

- (a) If the variance of a data set is zero, then all the observations in this data set are zero.
- (b) If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A AND B) = 0.9.
- (c) Assume X follows a continuous distribution which is symmetric about 0. If

, then .

- (d) A 95% confidence interval is wider than a 90% confidence interval of the same

parameter.

- (e) In a right-tailed test, the value of the test statistic is 1.5. If we know the test statistic

follows a Student’s t-distribution with P(T < 1.5) = 0.96, then we fail to reject the null hypothesis at 0.05 level of significance .

Refer to the following frequency distribution for Questions 2, 3, 4, and 5. Show all work

The frequency distribution below shows the distribution for checkout time (in minutes) in the MiniMart between 3:00 and 4:00 PM on a Friday afternoon.

Checkout Time (in minutes) | Frequency | Relative Frequency |

1.0 – 1.9 | 3 | |

2.0 – 2.9 | 12 | |

3.0 – 3.9 | 0.20 | |

4.0 – 4.9 | 3 | |

5.0 -5.9 | ||

Total | 25 |

2. Complete the frequency table with frequency and relative frequency. Express the relative

frequency to two decimal places.

3. What percentage of the checkout times was at least 3 minutes?

4. In what class interval must the median lie? Explain your answer.

5. Does this distribution have positive skew or negative skew? Why?

Refer to the following information for Questions 6 and 7. Show all work.

Consider selecting one card at a time from a 52-card deck. (Note: There are 4 aces in a deck of cards)

6. If the card selection is without replacement, what is the probability that the first card is an ace and the second card is also an ace? (Express the answer in simplest fraction form)

7. If the card selection is with replacement, what is the probability that the first card is an ace and the second card is also an ace? (Express the answer in simplest fraction form)

Refer to the following situation for Questions 8, 9, and 10.

The five-number summary below shows the grade distribution of two STAT quizzes for a sample of 500 students.

For each question, give your answer as one of the following:

(a) Quiz 1

(b) Quiz 2

(c) Both quizzes have the same value requested

(d) It is impossible to tell using only the given information.

Then explain your answer in each case.

- Which quiz has less interquartile range in grade distribution?
- Which quiz has the greater percentage of students with grades 90 and over?
- Which quiz has a greater percentage of students with grades less than 60?

Refer to the following information for Questions 11, 12, and 13. Show all work.

There are 1000 students in a high school. Among the 1000 students, 800 students have a laptop, and 300 students have a tablet. 150 students have both devices.

- What is the probability that a randomly selected student has neither device?
- What is the probability that a randomly selected student has a laptop, given that he/she

has a tablet?

- Let event A be the selected student having a laptop, and event B be the selected student

having a tablet. Are A and B independent events? Why or why not?

- A combination lock uses three distinctive numbers between 0 and 49 inclusive. How many different ways can a sequence of three numbers be selected? (Show work)
- Let random variable x represent the number of heads when a fair coin is tossed three

times. Show all work.

- (a) Construct a table describing the probability distribution.
- (b) Determine the mean and standard deviation of x. (Round the answer to two decimal places)

Minimum | Q1 | Median | Q3 | Maximum | |

Quiz 1 | 15 | 45 | 55 | 85 | 100 |

Quiz 2 | 20 | 35 | 50 | 90 | 100 |

16. Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opponent’s serves. Assume her opponent serves 10 times.

(a) Let X be the number of returns that Mimi gets. As we know, the distribution of X is a binomial probability distribution.

What is the number of trials (n), probability of successes (p) and

probability of failures (q), respectively?

(b) Find the probability that that she returns at least 1 of the 10 serves from her opponent.

(Show work)

Refer to the following information for Questions 17, 18, and 19. Show all work.

The lengths of mature jalapeño fruits are normally distributed with a mean of 3 inches and a standard deviation of 1 inch.

- What is the probability that a randomly selected mature jalapeño fruit is between 1.5 and 4 inches long?
- Find the 90th percentile of the jalapeño fruit length distribution.
- If a random sample of 100 mature jalapeño fruits is selected, what is the standard deviation of the

sample mean?

20. A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population standard deviation of the lifetime is 500 hours. Construct a 95% confidence interval estimate of the mean lifetime. Show all work. Just the answer, without supporting work, will receive no credit.

21. Consider the hypothesis test given by H0 :p=0.5

H1 : p < 0.5

In a random sample of 100 subjects, the sample proportion is found to be pˆ =0.45 .

- (a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
- (b) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.
- (c) Is there sufficient evidence to justify the rejection of H0 at the a= 0.01 level? Explain.

22. Consumption of large amounts of alcohol is known to increase reaction time. To investigate the effects of small amounts of alcohol, reaction time was recorded for five individuals before and after the consumption of 2 ounces of alcohol. Do the data below suggest that consumption of 2 ounces of alcohol increases mean reaction time?

Reaction Time (seconds) | |

Subject | Before After |

1 2 3 4 5 | 67 88 46 78 98 |

Assume we want to use a 0.01 significance level to test the claim.

- (a) Identify the null hypothesis and the alternative hypothesis.
- (b) Determine the test statistic. Show all work; writing the correct test statistic, without

supporting work, will receive no credit.

- (c) Determine the P-value. Show all work; writing the correct P-value, without

supporting work, will receive no credit.

- (d) Is there sufficient evidence to support the claim that consumption of 2 ounces of alcohol increases mean reaction time? Justify your conclusion.

23. The MiniMart sells four different types of Halloween candy bags. The manager reports that the four types are equally popular. Suppose that a sample of 500 purchases yields observed counts 150, 110, 130, and 110 for types 1, 2, 3, and 4, respectively.

Assume we want to use a 0.10 significance level to test the claim that the four types are equally popular.

(a) Identify the null hypothesis and the alternative hypothesis.

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(c) Determine the P-value for the test. Show all work; writing the correct P-value, without supporting work, will receive no credit.

(d) Is there sufficient evidence to support the manager’s claim that the four types are equally popular? Justify your answer.

Type | 1 | 2 | 3 | 4 |

Number of Bags | 150 | 110 | 130 | 110 |

24. A random sample of 4 professional athletes produced the following data where x is the number of endorsements the player has and y is the amount of money made (in millions of dollars).

- (a) Find an equation of the least squares regression line. Show all work; writing the correct equation, without supporting work, will receive no credit.
- (b) Based on the equation from part (a), what is the predicted value of y if x = 4? Show all work and justify your answer.

25. A STAT instructor is interested in whether there is any variation in the final exam grades between her two classes Data collected from the two classes are as follows:

Her null hypothesis and alternative hypothesis are:

- (a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
- (b) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.
- (c) Is there sufficient evidence to justify the rejection of H0 at the significance level of 0.05? Explain.

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