Question

Can someone please show me how to do this type of problem???

**Answers to Multiple-Choice Problems:** A student
wants to see if the correct answers to multiple choice problems are
evenly distributed. She heard a rumor that if you don't know the
answer, you should always *pick C*. In a sample of 100
multiple-choice questions from prior tests and quizzes, the
distribution of correct answers are given in the table below. In
all of these questions, there were four options {A, B, C, D}.

Correct Answers (* n* = 100)

A | B | C | D | |

Count | 22 | 24 | 33 | 21 |

**The Test:** Test the claim that correct answers
for all multiple-choice questions are not evenly distributed. Test
this claim at the 0.01 significance level.

(a) What is the null hypothesis for this test in terms of the probabilities of the outcomes?

*H*_{0}: *p*_{A} = 0.22,
*p*_{B} = 0.24, *p*_{C} = 0.33,
*p*_{D} = 0.21. *H*_{0}: The
probability of a correct answer being *C* is greater than
the others. *H*_{0}:
*p*_{A} = *p*_{B} =
*p*_{C} = *p*_{D} = 1/4.
*H*_{0}: At least one of the probabilities doesn't
equal 1/4.

(b) What is the value of the test statistic? **Round to 3
decimal places unless your software automatically rounds to 2
decimal places.**

*χ*^{2}

=

(c) Use software to get the P-value of the test statistic.
**Round to 4 decimal places unless your software
automatically rounds to 3 decimal places.**

P-value =

(d) What is the conclusion regarding the null hypothesis?

reject *H*_{0} fail to reject
*H*_{0}

(e) Choose the appropriate concluding statement.

We have proven that correct answers for all multiple-choice questions are evenly distributed. The data supports the claim that correct answers for all multiple-choice questions are not evenly distributed. There is not enough data to support the claim that correct answers for all multiple-choice questions are not evenly distributed.

Answer #1

The statistical software output for this problem is:

Hence,

a) *H*_{0}: *p*_{A} =
*p*_{B} = *p*_{C} =
*p*_{D} = 1/4. *H*_{0}: At least one
of the probabilities doesn't equal 1/4.

b) Test statistic = 3.6

c) P - value = 0.308

d) Fail to reject Ho

e) There is not enough data to support the claim that correct answers for all multiple-choice questions are not evenly distributed.

Answers to Multiple-Choice Problems: A student
wants to see if the correct answers to multiple choice problems are
evenly distributed. She heard a rumor that if you don't know the
answer, you should always pick C. In a sample of 100
multiple-choice questions from prior tests and quizzes, the
distribution of correct answers are given in the table below. In
all of these questions, there were four options {A, B, C, D}.
Correct Answers (n = 100)
A
B
C...

Answers to Multiple-Choice Problems: A student
wants to see if the correct answers to multiple choice problems are
evenly distributed. She heard a rumor that if you don't know the
answer, you should always pick C. In a sample of 100
multiple-choice questions from prior tests and quizzes, the
distribution of correct answers are given in the table below. In
all of these questions, there were four options {A, B, C, D}.
Correct Answers (n = 100)
A
B
C...

1. MY NOTES Answers to Multiple-Choice Problems: A student wants
to see if the correct answers to multiple choice problems are
evenly distributed. She heard a rumor that if you don't know the
answer, you should always pick C. In a sample of 100
multiple-choice questions from prior tests and quizzes, the
distribution of correct answers are given in the table below. In
all of these questions, there were four options {A, B, C, D}.
Correct Answers (n = 100)...

Answers to Multiple-Choice Problems: A student
wants to see if the correct answers to multiple choice problems are
evenly distributed. She heard a rumor that if you don't know the
answer, you should always pick C . In a sample of 100
multiple-choice questions from prior tests and quizzes, the
distribution of correct answers are given in the table below. In
all of these questions, there were four options {A, B, C, D}.
Correct Answers (n = 100)
A
B ...

Answers to Multiple-Choice Problems: A student
wants to see if the correct answers to multiple choice problems are
evenly distributed. She heard a rumor that if you don't know the
answer, you should always pick C . In a sample of 100
multiple-choice questions from prior tests and quizzes, the
distribution of correct answers are given in the table below. In
all of these questions, there were four options {A, B, C, D}.
Correct Answers (n = 100)
A
B ...

Customer Distribution by Weekday: A drop-in
auto repair shop staffs the same number of mechanics on every
weekday (weekends are not counted here). One of the mechanics
thinks this is a bad idea because he suspects the number of
customers is not evenly distributed across these days. For a sample
of 289 customers, the counts by weekday are given in the table.
Number of Customers by Day (n = 289)
Monday
Tuesday
Wednesday
Thursday
Friday
Count
53
68
55
65 ...

2.Customer Distribution by Weekday: A drop-in auto repair shop
staffs the same number of mechanics on every weekday (weekends are
not counted here). One of the mechanics thinks this is a bad idea
because he suspects the number of customers is not evenly
distributed across these days. For a sample of 289 customers, the
counts by weekday are given in the table. Number of Customers by
Day (n = 289) Monday Tuesday Wednesday Thursday Friday Count 55 66
59 63...

Customer Distribution by Weekday: A drop-in
auto repair shop staffs the same number of mechanics on every
weekday (weekends are not counted here). One of the mechanics
thinks this is a bad idea because he suspects the number of
customers is not evenly distributed across these days. For a sample
of 289 customers, the counts by weekday are given in the table.
Number of Customers by Day (n = 289)
Monday
Tuesday
Wednesday
Thursday
Friday
Count
55
68
59
67 ...

Multiple Choice Strategy: Some students have
suggested that if you have to guess on a multiple-choice question,
you should always choose C. Carl, the student, wants to
investigate this theory. He is able to get a sample of past tests
and quizzes from various teachers. In this sample there are 90
multiple-choice questions with four options (A, B, C, D).
The distribution of correct answers from this sample is given in
the frequency table below.
Correct
Answer
Frequency
A
16...

You are conducting a multinomial Goodness of Fit hypothesis test
for the claim that the 4 categories occur with the following
frequencies:
HoHo :
pA=0.4pA0.4; pB=0.25pB0.25; pC=0.25pC0.25; pD=0.1pD0.1
Complete the table. Report all answers accurate to two decimal
places, unless otherwise specified.
Category
Observed
Frequency
Expected
Frequency
A
39
B
18
C
30
D
7
What is the chi-square test-statistic for this data? (Round to two
decimal places)
χ2=χ2
What is the P-Value? (Round to four decimal places)
P-Value =

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