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Statistic Final Exam - Student of Fortune

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					1. An automotive manufacturer claims the mean price of a small suv is at most $26,014. If a hypothesis
test is performed, how should you interpret a decision that (a) rejects the null hypothesis and (b) fails to
reject the null hypothesis?



(a) Choose the correct answer below.

1. There is enough evidence to support the claim that the mean price of a small SUV is at most $26,014.

2. There is sufficient evidence to indicate that the claim that the mean price of a small suv is at most
$26n014 is false.

3. There is not enough evidence to support the claim that the mean price of a small SUV is at most
$26,014

4. There is insufficient evidence to indicate that the claim that the mean price of a small suv is at most
$26,014 is false.



(b) Choose the correct answer below

1. There is enough evidence to support the claim that the mean price of a small suv is at most $26,014.

2. There is insufficient evidence to indicate that the calim that the mean price of a small suv is at most
$26,014 is false.

3. There is not enough evidence to support the calim that the mean price of a small suv is at most
$26,014

4. There is sufficient evidence to indicate that the calim that the mean price of a small suv is at most
$26,014 is false.



2. In a recent year, scores on a standardized test for high school students with a 3.50 to 4.00 grade point
average were normall distributed, with a mean of 38.8 and a standard deviation of 1.8. A student with a
3.50 to 4.00 grade point average who took the standardized test is randomly selected.

a(a) Find the probability that the student's test score is less than 35.

The probability of a student scoring less than 35 is = (round to four decimal places as needed)

(b) Find tthe probability tthat tthe students test score is between 36.1 and 41.5.

The probability of a student scoring between 36.1 and 41.5 is= (round to four decimal places as needed)

(c) Find the probability that the student's test score is more than 40.2

The probability of a student scoring more than 40.2 is = (round to four decimal places as needed.)
3. The lenghts of the first 10 words of 2 books are listed below. Find the range, variance, and standard
deviation for each of the two samples, then compare the two sets of results. Does there appear to be a
difference in variation?

Book 1: 2 5 4 6 3 2 4 2 3

Book 2: 9 12 9 10 7 9 12 11 10 10



Find the range for book 1

Range=       letters

Find the range for book 2

Range=      letters



Find the variance and standard deviation for book 1

Sample variance = letters2 (Round to one decimal place as needed)

Sample standard deviation =        letters (Do not round until the final answer. Then round to one decimal
place as needed.)

Find the variance and standard deviation for book 2

Sample variance= letters2

Sample variance= Leters (round to one decimal place as needed)

sample standard deviation = letters (Do not round until the final answer. Then round to one decimal
place as needed.)

Is there a difference in variation between the two books?

a. Yes, there is much less variation amoung th word lenghts in book 1

b. Yes, there is much less variation among the word lengths in book 2

c. No, there is not a difference in the variation



4.Use the contingency table to the right to calculate the marginal frequencies and find the expected
frequency for each cell in the contingency table. Assuem that the variables are independent.



Result           Stretched           No stretched
Indury              25                       30

No injury            201                   184



(a) Calculate the marginal frequencies and sample size. (Fill in question marks)

Result              Stretched           No stretched         Total

Injury                   25                       30                 ?

No injury                201                     184          ?


Total                    ?                         ?                 ?

(b) Find the expected frequency for each cell in the contingency table. (round to two decimal places as
needed.)

Restult                  Stretched          Not stretched

Injury                         ?                       ?

No injury                      ?                   ?



5. Use the confidence interval to find the margin of error and the sample mean. (0..72, 0.510)

The margin of error is=

The sample mean is =



6. Find the mean, variance and standard deviation fo the binomial distribution with the given values of n
an p. n= 126, p=0.52

a. The mean m is = (round to the nearest tenth as needed)

b. the variance, o2, is = (round to the nearest tenth as needed)

c. the standard deviation, o, is = (round to the nearest tenth as needed)



7. Test the calim below about the mean of the difference of two populations. Use a t-test for dependent,
random samples at the given level of significance with the given statistics. Is the test right-tailed, left-
tailed, or two-tailed? Assume the populations are normally distributed.

Claim: Mo=O , a=0.01. Statistics:d=3.5, sd=8045, n=10

a. Is the test right-tailed, left tailed, or two-tailed?
b. Should the null hypothesis be rejected?

fail to reject Ho

reject Ho



8. Test the claim about the differences between two population variances 02/1 at the given level of
significance o using the given sample statistics. Assume that the sample statistics are from independent
samples that are randomly selected and each population has a normal distribution.

Claim:02/1>02/2, a=0.05

Sample statistics: s2/1=843, n1=5,s2/2=473,n2=6

Choose the correct answer below

. fail to reject the null hypothesis. There is not enough evidence to support the claim

.reject the null hypothesis. There is enough evidence to reject the calim

.fail to reject the null hpothesis. There is not enough evidence to reject the calim

.Reject the null hypothesis. There is enough evidence to support the claim



9. The mean exam score for 44 high schoold students is 24.3 and the standard deviation is 4.7. The
mean exam score for the 58 female high school students is 21.3 and the standard deviation is 4.1. At
0=0.01, can you reject the claim that the male and female hgih school students have equal exam
scores? Complete parts (a) through (e).

What is the Claim?

a. Male high school students have greater exam scores than feamle students.

b. Male high school students have lower exam scores than female students.

c. Male and female high schoold students have equal exam scores

d. Male and female high school students have different exam scores.



What are Ho and Ha?

a. Ho:M1<M2          C. Ho:M1>M2               D. Ho:M1_<M2      E. Ho:M1=M2

   Ha:M1_>M2              Ha:M1_<M2                Ha:M1>M2           Ha:M1=/M2

B. Ho:M1_>M2         F. Ho:M1=/M2

   Ha:M1<M2               Ha:M1=M2
Find the critical value(s) and identify the rejection region(S)

The critical value(s) is/are= (round to three decimal places as needed. use a comma to separate
answers as needed.)



What is/are the rejection region(s)?

a. z<-2.575, z>2.575

b. z<1.645,z>1.645

e. z<-3.08,z>-3.08

f. z>2.575

Find the standardized test statistic z. z= (round to three decimal places as needed)

Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below.

a. Fail to reject H0. The standardized test statistic is not in the rejection region

b. Reject Ho. The standardized test statistic is not in the rejection region

c. Fail to reject Ho. The standardized test statistic is in the rejection region.

d. Reject Ho. The standardized test statistic is in the rejection region



Interpret the decision in the context of the orginial claim.

At the _% significance level, ther is ______(suffiecient or insufficeint evidence to (support,or reject)the
claim that male high school students have exam scores_________(equal,greater, less than) to female
high school students exam scores.

				
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