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...

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 ...

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 =

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 110
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
21...

Pro-choice/Pro-life and Region of the Country:
The results of a 2013 Gallup poll about people's position on
abortion (pro-life or pro-choice) by region of the country are
summarized in the contingency table below.
Observed Frequencies:
Oi's
East
Midwest
South
West
Totals
Pro-Choice
215
96
181
184
676
Pro-Life
191
86
239
208
724
Totals
406
182
420
392
1400
The Test: Test whether or not there is a
dependent relationship between abortion stance and region. Conduct
this test...

Pro-choice/Pro-life and Region of the Country:
The results of a 2013 Gallup poll about people's position on
abortion (pro-life or pro-choice) by region of the country are
summarized in the contingency table below.
Observed Frequencies:
Oi's
East
Midwest
South
West
Totals
Pro-Choice
200
96
169
211
676
Pro-Life
178
86
223
237
724
Totals
378
182
392
448
1400
The Test: Test whether or not there is a
dependent relationship between abortion stance and region. Conduct
this test at the...

Suppose the makers of M&M candies give the following average
percentages for the mix of colors in their bags of plain chocolate
M&M's.
Stated Distribution of Colors
Brown
Yellow
Red
Orange
Green
Blue
Percent
30%
20%
20%
10%
10%
10%
Now, you randomly select 200 M&M's and get the counts given
in the table below. You expected about 20 blues but only got 8. You
suspect that the maker's claim is not true.
Observed Counts by Color...

M&M's Color Distribution: Suppose the
makers of M&M candies give the following average percentages
for the mix of colors in their bags of plain chocolate
M&M's.
Stated Distribution of Colors
Brown
Yellow
Red
Orange
Green
Blue
Percent
30%
20%
20%
10%
10%
10%
Now, you randomly select 200 M&M's and get the counts given
in the table below. You expected about 20 blues but only got 9. You
suspect that the maker's claim is not true.
Observed Counts by Color...

M&M's Color Distribution: Suppose the
makers of M&M candies give the following average percentages
for the mix of colors in their bags of plain chocolate
M&M's.
Stated Distribution of Colors
Brown
Yellow
Red
Orange
Green
Blue
Percent
30%
20%
20%
10%
10%
10%
Now, you randomly select 200 M&M's and get the counts given
in the table below. You expected about 20 blues but only got 9. You
suspect that the maker's claim is not true.
Observed Counts by Color...

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