In a large class of introductory Statistics students, the professor has each person toss a coin 26 times and calculate the proportion of his or her tosses that were heads. Complete parts a through d below. a) Confirm that you can use a Normal model here. The Independence Assumption is satisfied because the sample proportions are are are not independent of each other since one sample proportion does not affect can affect does not affect another sample proportion. The Success/Failure Condition is is not is satisfied because np=1313 and nq=1313, which are both greater than or equal to greater than or equal to less than 10. (Type integers or decimals. Do not round.) b) Use the 68–95–99.7 Rule to describe the sampling distribution model. About 68% of the students should have proportions between nothing and nothing, about 95% between nothing and nothing, and about 99.7% between nothing and nothing. (Type integers or decimals rounded to four decimal places as needed. Use ascending order.) c) They increase the number of tosses to 55 each. Draw and label the appropriate sampling distribution model. Check the appropriate conditions to justify your model. The Independence Assumption is is is not satisfied because the sample proportions are are not are independent of each other since one sample proportion does not affect does not affect can affect another sample proportion. The Success/Failure Condition is is is not satisfied because np=2828 and nq=2828, which are both greater than or equal to less than greater than or equal to 10. (Type integers or decimals. Do not round.) Use the graph below to describe the sampling distribution model. p-hatRange ARange BRange C A symmetric bell-shaped curve is plotted above a horizontal axis labeled p-hat, which has 7 unlabeled tick marks in equal increments. A dashed vertical line segment runs from the axis to the curve at its center and peak at the center tick mark, and solid vertical line segments run from the axis to the curve at each of the other 6 tick marks. Total areas under the curve between solid line segments are labeled as follows: between the innermost solid line segments, Range A; between the middle line segment on the left half and the middle line segment on the right half, Range B; between the outermost line segments, Range C. The curve is nearly horizontal and just above the axis at the outermost line segments. Range A, which corresponds to nothing% of the proportions, spans from nothing and nothing. Range B, which corresponds to nothing% of the proportions, spans from nothing and nothing. Range C, which corresponds to nothing% of the proportions, spans from nothing and nothing. (Type integers or decimals rounded to four decimal places as needed. Use ascending order.) d) Explain how the sampling distribution model changes as the number of tosses increases. A. The sampling distribution model becomes wider because the standard deviation of the distribution will increase. B. The sampling distribution model becomes narrower because the standard deviation of the distribution will decrease. C. The sampling distribution model shifts to the left because the mean of the distribution will decrease. D. The sampling distribution model shifts to the right because the mean of the distribution will increase.

In a large class of introductory Statistics students, the professor has each person toss a coin 26 times and calculate the proportion of his or her tosses that were heads. Complete parts a through d below. a) Confirm that you can use a Normal model here. The Independence Assumption is satisfied because the sample proportions are are are not independent of each other since one sample proportion does not affect can affect does not affect another sample proportion. The Success/Failure Condition is is not is satisfied because np=1313 and nq=1313, which are both greater than or equal to greater than or equal to less than 10. (Type integers or decimals. Do not round.) b) Use the 68–95–99.7 Rule to describe the sampling distribution model. About 68% of the students should have proportions between nothing and nothing, about 95% between nothing and nothing, and about 99.7% between nothing and nothing. (Type integers or decimals rounded to four decimal places as needed. Use ascending order.) c) They increase the number of tosses to 55 each. Draw and label the appropriate sampling distribution model. Check the appropriate conditions to justify your model. The Independence Assumption is is is not satisfied because the sample proportions are are not are independent of each other since one sample proportion does not affect does not affect can affect another sample proportion. The Success/Failure Condition is is is not satisfied because np=2828 and nq=2828, which are both greater than or equal to less than greater than or equal to 10. (Type integers or decimals. Do not round.) Use the graph below to describe the sampling distribution model. p-hatRange ARange BRange C A symmetric bell-shaped curve is plotted above a horizontal axis labeled p-hat, which has 7 unlabeled tick marks in equal increments. A dashed vertical line segment runs from the axis to the curve at its center and peak at the center tick mark, and solid vertical line segments run from the axis to the curve at each of the other 6 tick marks. Total areas under the curve between solid line segments are labeled as follows: between the innermost solid line segments, Range A; between the middle line segment on the left half and the middle line segment on the right half, Range B; between the outermost line segments, Range C. The curve is nearly horizontal and just above the axis at the outermost line segments. Range A, which corresponds to nothing% of the proportions, spans from nothing and nothing. Range B, which corresponds to nothing% of the proportions, spans from nothing and nothing. Range C, which corresponds to nothing% of the proportions, spans from nothing and nothing. (Type integers or decimals rounded to four decimal places as needed. Use ascending order.) d) Explain how the sampling distribution model changes as the number of tosses increases. A. The sampling distribution model becomes wider because the standard deviation of the distribution will increase. B. The sampling distribution model becomes narrower because the standard deviation of the distribution will decrease. C. The sampling distribution model shifts to the left because the mean of the distribution will decrease. D. The sampling distribution model shifts to the right because the mean of the distribution will increase.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

See similar textbooks

Related questions

Concept explainers

Question

In a large class of introductory Statistics students, the professor has each person toss a coin

times and calculate the proportion of his or her tosses that were heads. Complete parts a through d below.

a) Confirm that you can use a Normal model here.

The Independence Assumption

satisfied because the sample proportions

are

are not

independent of each other since one sample proportion

does not affect

can affect

does not affect

another sample proportion. The Success/Failure Condition

is not

satisfied because

np=1313

and

nq=1313,

which are both

greater than or equal to

less than

10.

(Type integers or decimals. Do not round.)

b) Use the

68–95–99.7

Rule to describe the sampling distribution model.

About 68% of the students should have proportions between

nothing

and

nothing,

about 95% between

nothing

and

nothing,

and about 99.7% between

nothing

and

nothing.

(Type integers or decimals rounded to four decimal places as needed. Use ascending order.)

c) They increase the number of tosses to

each. Draw and label the appropriate sampling distribution model. Check the appropriate conditions to justify your model.

The Independence Assumption

is not

satisfied because the sample proportions

are

are not

are

independent of each other since one sample proportion

does not affect

can affect

another sample proportion. The Success/Failure Condition

is not

satisfied because

np=2828

and

nq=2828,

which are both

greater than or equal to

less than

greater than or equal to

10.

(Type integers or decimals. Do not round.)

Use the graph below to describe the sampling distribution model.

p-hatRange ARange BRange C

A symmetric bell-shaped curve is plotted above a horizontal axis labeled p-hat, which has 7 unlabeled tick marks in equal increments. A dashed vertical line segment runs from the axis to the curve at its center and peak at the center tick mark, and solid vertical line segments run from the axis to the curve at each of the other 6 tick marks. Total areas under the curve between solid line segments are labeled as follows: between the innermost solid line segments, Range A; between the middle line segment on the left half and the middle line segment on the right half, Range B; between the outermost line segments, Range C. The curve is nearly horizontal and just above the axis at the outermost line segments.

Range A, which corresponds to

nothing%

of the proportions, spans from

nothing

and

nothing.

Range B, which corresponds to

nothing%

of the proportions, spans from

nothing

and

nothing.

Range C, which corresponds to

nothing%

of the proportions, spans from

nothing

and

nothing.

(Type integers or decimals rounded to four decimal places as needed. Use ascending order.)

d) Explain how the sampling distribution model changes as the number of tosses increases.

The sampling distribution model becomes wider because the standard deviation of the distribution will increase.

The sampling distribution model becomes narrower because the standard deviation of the distribution will decrease.

The sampling distribution model shifts to the left because the mean of the distribution will decrease.

The sampling distribution model shifts to the right because the mean of the distribution will increase.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Glencoe Algebra 1, Student Edition, 9780079039897…

Algebra

ISBN:

9780079039897

Author:

Carter

Publisher:

McGraw Hill