Question

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 80 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 | 14 |

B | 18 |

C | 33 |

D | 15 |

(a) If the correct answers for all multiple-choice problems are
uniformly distributed across the four options (*A, B, C,
D*), what is the theoretical proportion of those which should
have the answer *C*? **Express your answer as an exact
decimal, not a percentage.**

(b) Based on the sample that Carl collected, what is the point
estimate for the proportion of all multiple-choice questions with a
correct answer of *C*? **Round your answer to 3
decimal places.**

(c) What is the critical value of *z* (denoted
*z*_{α/2}) for a 99% confidence interval?
**Use the value from the table or, if using software, round
to 2 decimal places.**

*z*_{α/2} =

(d) What is the margin of error (*E*) for a 99% confidence
interval? **Round your answer to 3 decimal
places.**

*E* =

(e) Construct the 99% confidence interval for the proportion of
**all** multiple-choice questions with a correct
answer of *C*? **Round your answers to 3 decimal
places.**

< *p* <

(f) Can Carl be 99% confident that the correct answer of *C*
shows up more frequently than the theoretical value found in part
(a) would suggest?

No, because 0.25 is within the confidence interval limits.

Yes, because 0.25 is below the lower limit of the confidence interval.

No, because 0.25 is below the lower limit of the confidence interval.

Yes, because 0.25 is within the confidence interval limits.

Answer #1

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...

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...

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
17...

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...

Corn: In a random sample of 88 ears of corn,
farmer Carl finds that 15 of them have worms. He wants to find the
99%confidence interval for the proportion of all his corn that has
worms.
(a) What is the point estimate for the proportion of all of
Carl's corn that has worms? Round your answer to 3 decimal
places.
(b) What is the critical value of z (denoted
zα/2) for a 99% confidence interval?
Use the value from the...

Corn: In a random sample of 88 ears of corn, farmer Carl finds
that 14 of them have worms. He wants to find the 99% confidence
interval for the proportion of all his corn that has worms.
(a) What is the point estimate for the proportion of all of Carl's
corn that has worms? Round your answer to 3 decimal places.
(b) What is the critical value of z (denoted zα/2) for a 99%
confidence interval? Use the value...

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 ...

Pinworm: In a random sample of 790 adults in the U.S.A., it
was found that 76 of those had a pinworm infestation. You want to
find the 99% confidence interval for the proportion of all U.S.
adults with pinworm.
(a) What is the point estimate for the proportion of all U.S.
adults with pinworm? Round your answer to 3 decimal places.
(b) What is the critical value of z (denoted zα/2) for a 99%
confidence interval? Use the value...

Corn: In a random sample of 84 ears of corn, farmer Carl finds
that 7 of them have worms. He wants to find the 90% confidence
interval for the proportion of all his corn that has worms.
(a) What is the point estimate for the proportion of all of
Carl's corn that has worms? Round your answer to 3 decimal places.
____
(b) What is the critical value of z (denoted zα/2) for a 90%
confidence interval? Use the value...

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