Statistics

1, 3, 5, 7 and 9 are odd and 0, 2, 4, 6, and 8 are even. Consider a

60-digit

line from a random number table. Complete parts (a) and (b) below.

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Part 1

a. How many of the

digits would you expect to be

even,

on average?

(Type an integer or a decimal. Do not round.)

Part 2

b. If you actually counted, would you get exactly the number predicted in part (a)? Explain.

Yes, because samples will always match the population proportion.

Yes, because the sample is sufficiently large that the sample proportion will be the same as the population proportion.

No, because samples will never have exactly the number predicted due to variation from sample to sample.

No, because while a sample might have exactly the number predicted, a sample could also have smaller or larger numbers due to variation from sample to sample.

According to a poll,

37%

of Americans read print books exclusively (rather than reading some digital books). Suppose a random sample of

300

Americans is selected. Complete parts (a) through (d) below.

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Part 1

a. What percentage of the sample would we expect to read print books exclusively?

37%

Part 2

b. Verify that the conditions of the Central Limit Theorem are met.

The Random and Independent condition

holds assuming independence.

holds through an exception.

holds assuming independence.

does not hold.

The Large Samples condition

holds.

does not hold.

holds.

The Big Populations condition

can

cannot

reasonably be assumed to hold.

Part 3

c. What is the standard error for this sample proportion?

SEequals0.028

(Type an integer or decimal rounded to three decimal places as needed.)

Part 4

d. Complete this sentence:

We expect

12.3%

of Americans to read print books exclusively, give or take

2.8%.

(Type integers or decimals rounded to one decimal place as needed.)

In 2018 it was estimated that approximately

48%

of the American population watches the Super Bowl yearly. Suppose a sample of

122

Americans is randomly selected. After verifying the conditions for the Central Limit Theorem are met, find the probability that the majority (more than

50%)

watched the Super Bowl.

Question content area bottom

Part 1

First, verify that the conditions of the Central Limit Theorem are met.

The Random and Independent condition

holds assuming independence.

does not hold.

holds through an exception.

holds assuming independence.

The Large Samples condition

holds.

does not hold.

The Big Populations condition

can

cannot

can

reasonably be assumed to hold.

Part 2

The probability is

0.332.

(Type an integer or decimal rounded to three decimal places as needed.)

A random sample of likely voters showed that

47%

planned to support Measure X. The margin of error is

percentage points with a

99%

confidence level. Complete parts (a) through (c) below.

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Part 1

a. Use a carefully worded sentence to report the

99%

confidence interval for the percentage of voters who plan to support Measure X.

▼

There is a 99% chance

There is a 1% chance

I am 1% confident

I am 99% confident

that the

▼

population percentage

sample percentage

standard deviation of the percentage

of likely voters who plan to support Measure X is between

enter your response here%

and

enter your response here%.

(Use ascending order.)

Part 2

b. Is there evidence that Measure X will

fail?

▼

No, there is not

Yes, there is

evidence that Measure X will

fail,

since

▼

not all

all

percentages within the confidence interval are

▼

less

greater

than

▼

100%.

0%.

1%.

50%.

99%.

Part 3

c. Suppose the survey was taken on the streets of the most populous city of a state and the measure was a statewide measure. Explain how that would affect your conclusion.

The survey would

▼

suffer from sampling bias.

suffer from a biased estimator.

not suffer from any bias.

suffer from measurement bias.

The answer from part (a) would be

▼

valid only for the population of people on the streets of the city.

valid for the population of the state.

invalid with respect to any population.

A confidence interval resulting from such a survey

▼

does in this case

can, but in this case does not

cannot

provide strong evidence about whether Measure X will succeed or fail in the state; the conclusion in part (b)

▼

does not hold.

holds.

	Preschool	No Preschool
Grad HS	37	23
No Grad HS	25	41

In a study,

126

children of a certain race in a certain city were randomly assigned to one of two groups: one group enrolled in a preschool, and the other group did not. A research question was whether attendance at preschool had an effect on high school graduation. The accompanying table shows whether the students graduated from regular high school or not and includes both boys and girls. Find a

95%

confidence interval for the difference in proportions, and interpret it.

Click the icon to view the data.

Question content area bottom

Part 1

Step 1: Calculate percentages

Looking at children who went to preschool,

StartFraction 37 Over 62 EndFraction,

59.7%,

graduated from high school. Looking at the children who did not go to preschool, what percent graduated from high school?

enter your response here%

of children who did not go to preschool graduated from high school.

(Round to one decimal place as needed.)

Part 2

Step 2: Compare

In this sample, the children who attend preschool are

▼

less

likely to graduate than the children who don't attend preschool.

Part 3

Step 3: Verify conditions

Although we don't have a random sample of children, we do have random assignment to groups, and the two groups are independent.

We must verify that the sample sizes are large enough. Let sample 1 be children who went to preschool and let sample 2 be children who did not go to preschool.

n 1 ModifyingAbove p with caret 1equals62 left parenthesis 0.597 right parenthesisequals37

n 1 left parenthesis 1 minus ModifyingAbove p with caret 1 right parenthesisequals62 left parenthesis 0.403 right parenthesisequals25

n 2 ModifyingAbove p with caret 2equals64 left parenthesis 0.359 right parenthesisequalsenter your response here

n 2 left parenthesis 1 minus ModifyingAbove p with caret 2 right parenthesisequalsenter your response here

(Round to the nearest integer as needed.)

Part 4

Step 4: Calculate intervals

The

95%

confidence interval for the difference

(p Subscript 1minusp Subscript 2)

left parenthesis nothing,nothing right parenthesis.

(Round to three decimal places as needed.)

Part 5

Step 5: Draw Conclusions

The interval

▼

captures

does not capture

0, suggesting that it

▼

is not

plausible that the proportions are the same.

Part 6

Step 6: Generalize

Can we generalize to a larger population from this data set? Why or why not?

▼

Yes, we can

No, we cannot

generalize to a larger population from this data set, since this study

▼

used

did not use

▼

large samples.

random sampling.

random assignment.

independent samples.

Part 7

Step 7: Determine causation

Can we conclude from this data set that preschool caused the difference? Why or why not?

▼

No, we cannot

Yes, we can

conclude from this data set that the preschool caused the difference, since this study

▼

did not use

used

▼

independent samples.

large samples.

random assignment.

random sampling.

Looking at the children who did not go to preschool, what percent graduated from high school?(Round to one decimal place as needed.)In this sample, the children who attend preschool arelikely to graduate than the children who don't attend preschool.n 2 ModifyingAbove p with caret 264 left parenthesis 0.359 right parenthesisn 2 left parenthesis 1 minus ModifyingAbove p with caret 2 right parenthesisn 2 left parenthesis 1 minus ModifyingAbove p with caret 2 right parenthesis(Round to the nearest integer as needed.)))The interval0, suggesting that it0, suggesting that itplausible that the proportions are the same.Why or why not?generalize to a larger population from this data set, since this studygeneralize to a larger population from this data set, since this studyplausible that the proportions are the same.Why or why not?conclude from this data set that the preschool caused the difference, since this studyconclude from this data set that the preschool caused the difference, since this studylistbox 9,