Expert answer:I need help with my statistics final assignment.
Answer & Explanation:Final Weekstat_final_week.docx
stat_final_week.docx
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1. True or False. Justify for full credit. (15 pts)
.
(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. Just the answer, without supporting work, will
receive no credit.
The frequency distribution below shows the distribution for checkout
time (in minutes) in MiniMart between 3:00 and 4:00 PM on a Friday
afternoon.
Checkout Time (in
minutes)
Frequency
1.0 - 1.9
3
2.0 - 2.9
12
3.0 - 3.9
Relative
Frequency
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?
(5 pts) (3 pts)
(5 pts) (2 pts)
Refer to the following information for Questions 6 and 7. Show all
work. Just the answer, without supporting work, will receive no credit.
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) (5 pts)
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) (5 pts)
Refer to the following situation for Questions 8, 9, and 10.
The five-number summary below shows the grade distribution of two
STAT 200 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. (4 pts each)
8.
Which quiz has less interquartile range in grade distribution?
9.
Which quiz has the greater percentage of students with grades 80
or over?
10.
Which quiz has a greater percentage of students with grades less
than or equal to 50?
Refer to the following information for Questions 11, 12, and 13. Show
all work. Just the answer, without supporting work, will receive no
credit.
There are 1000 students in a high school. Among the 1000 students,
800 students have a laptop, and 300 students have a tablet. 250 students
have both devices.
11.
What is the probability that a randomly selected student has
neither device? (10 pts)
12.
What is the probability that a randomly selected student has a
tablet, given that he/she has a laptop? (5 pts)
13.
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? (5 pts)
14.
A combination lock uses three distinctive numbers between 0 and
39 inclusive. How many different ways can a sequence of three
numbers be selected? (Show work) (5 pts)
15.
Let random variable x represent the number of heads when a fair
coin is tossed three
times. Show all work. Just the answer, without supporting work, will
receive no credit.
.
(a) Construct a table describing the probability distribution. (5 pts)
.
(b) Determine the mean and standard deviation of x. (Round the
answer to two decimal places) (10 pts)
16. Mimi just started her tennis class three weeks ago. On average, she
is able to return 25% 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. Just the answer, without supporting work, will receive no
credit.
(5 pts) (10 pts)
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 3.5 inches long? (5 pts)
. Find the 90th percentile of the jalapeño fruit length distribution. (5 pts)
. If a random sample of 400 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 90% confidence interval estimate of the mean
lifetime. Show all work. Just the answer, without supporting work, will
receive no credit. (8 pts)
21. Consider the hypothesis test given by H0 :p=0.5
H1 : p 0.5
In a random sample of 400 subjects, the sample proportion is found to
be pˆ = 0.55 .
6. (a)
Determine the test statistic. Show all work; writing the correct
test statistic, without supporting work, will receive no credit.
7. (b)
Determine the P-value for this test. Show all work; writing the
correct P-value, without supporting work, will receive no credit.
8. (c)
Is there sufficient evidence to justify the rejection of H0 at the
= 0.01 level? Explain. (15 pts)
(5 pts)
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)
Subjec
Before After
t
1234
67 88 46 79 98
5
Assume we want to use a 0.05 significance level to test the claim.
11.
(a) Identify the null hypothesis and the alternative hypothesis.
12.
(b) Determine the test statistic. Show all work; writing the
correct test statistic, without supporting work, will receive no
credit.
13.
(c) Determine the P-value. Show all work; writing the correct Pvalue, without supporting work, will receive no credit.
14.
(d) Is there sufficient evidence to support the claim that
consumption of 2 ounces of alcohol increases mean reaction
time? Justify your conclusion. (15 pts)
23. The MiniMart sells five different types of coffee mugs. The
manager reports that the five types are equally popular. Suppose that a
sample of 500 purchases yields observed counts 110, 100, 110, 100,
and 80 for types 1, 2, 3, 4, and 5, respectively.
Assume we want to use a 0.05 significance level to test the claim that
the five 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.
(15 pts)
Type
1
2
3
4
5
Number of
Mugs
110
100
110
100
80
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).
16.
(a) Find an equation of the least squares regression line. Show all
work; writing the correct equation, without supporting work, will
receive no credit. (10 pts)
17.
(b) Based on the equation from part (a), what is the predicted
value of y if x = 2? Show all work and justify your answer. (5
pts)
25. A STAT 200 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. (10 pts)
...
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