Graded Homework

This week we must read

Lane et al. Chapter 15&Illowskyet
al.Chapter 13

Do the four problems listed in the table
below.

Please submit them in your Assignment
Folder for grading.

eResources

Chapter

Problem

Page*

Illowsky et al.

13

69

p.
717

ANOVA

71

p.
718

ANOVA

77

p.
721

F-test for two Variances

81

p.
722

F-test for two Variances

* Page numbers are approximated due to
version control of the eResources, especially for Illowsky et al.

For each problem you must submit the
following information in the order given and you must identify each item by
number.

1. State both hypotheses and identify the
claim.

2. Give the F-statistic.

3. Give the p-value

4. Give the comparison and the decision

5. State a conclusion in plain English as
related to the claim.

You can get a items #2 and #3 from
technology, and maybe #4. But you must supply #1 and #2 yourself.

I recommend using Excel or other technology
but DO NOT submit the output. Read it carefully and extract the above
information that you need to perform the test.

If you don’t follow the above instructions
there will be penalty.

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
H₀: ?1 = ?2 = ?3 = ?4 = ?5

Alternate
Hypothesis is H_?: At least any two of the group means ?1, ?2, …, ?5
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.

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

, then .

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

parameter.

1. (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.

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.

8. Which quiz has less interquartile range in
grade distribution?

9. Which quiz has the greater percentage of
students with grades 90 and over?

10. 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.

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

has a tablet?

1. 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?

1. 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)
2. Let random variable x represent the
   number of heads when a fair coin is tossed three

times. Show all
work.

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

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 jalapen?o fruits are normally distributed with a mean of 3 inches and a
standard deviation of 1 inch.

1. What is the probability that a
   randomly selected mature jalapen?o fruit is between 1.5 and 4 inches long?
2. Find the 90th percentile of the
   jalapen?o fruit length distribution.
3. If a random sample of 100 mature
   jalapen?o 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 .

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

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

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

supporting work,
will receive no credit.

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

supporting work,
will receive no credit.

1. (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.

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).

1. (a) Find an equation of the
   least squares regression line. Show all work; writing the correct
   equation, without supporting work, will receive no credit.
2. (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:

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