In a large class of introductory Statistics students, the professor has each person toss a coin 33 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 not is satisfied because the sample proportions ▼ are are not independent of each other since one sample proportion ▼ does not affect can affect another sample proportion. The Success/Failure Condition ▼ is not is satisfied because np=nothing and nq=nothing, which are both ▼ less than greater than or equal to 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 77 each. Draw and label the appropriate sampling distribution model. Check the appropriate conditions to justify your model. The Independence Assumption ▼ is not is satisfied because the sample proportions ▼ are not are independent of each other since one sample proportion ▼ can affect does not affect another sample proportion. The Success/Failure Condition ▼ is is not satisfied because np=nothing and nq=nothing, which are both ▼ greater than or equal to less than 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 shifts to the right because the mean 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 becomes wider because the standard deviation of the distribution will increase. D. The sampling distribution model shifts to the left because the mean of the distribution will decrease.

In a large class of introductory Statistics students, the professor has each person toss a coin 33 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 not is satisfied because the sample proportions ▼ are are not independent of each other since one sample proportion ▼ does not affect can affect another sample proportion. The Success/Failure Condition ▼ is not is satisfied because np=nothing and nq=nothing, which are both ▼ less than greater than or equal to 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 77 each. Draw and label the appropriate sampling distribution model. Check the appropriate conditions to justify your model. The Independence Assumption ▼ is not is satisfied because the sample proportions ▼ are not are independent of each other since one sample proportion ▼ can affect does not affect another sample proportion. The Success/Failure Condition ▼ is is not satisfied because np=nothing and nq=nothing, which are both ▼ greater than or equal to less than 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 shifts to the right because the mean 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 becomes wider because the standard deviation of the distribution will increase. D. The sampling distribution model shifts to the left because the mean of the distribution will decrease.

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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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

▼

is not

satisfied because the sample proportions

▼

are

are not

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=nothing

and

nq=nothing,

which are both

▼

less than

greater than or equal to

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 not

are

independent of each other since one sample proportion

▼

can affect

does not affect

another sample proportion. The Success/Failure Condition

▼

is not

satisfied because

np=nothing

and

nq=nothing,

which are both

▼

greater than or equal to

less than

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 shifts to the right because the mean of the distribution will increase.

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

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

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

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