Statistics 121 Exam 1 | Complete Solution

Which numerical summary is used for categorical data?

Select one:

a. meanb. medianc. proportiond. standard deviation

Question 2

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The following situation applies to Questions 2-4:
A study of religious practices among college students interviewed a sample of 127 students; 107 of the students said that they prayed at least once in a while.

Which of the following best describes the population?

Select one:

a. All college studentsb. All college student who believe in a higher powerc. All college students who pray at least once in a whiled. All the people who pray at least once in a while

Question 3

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Which of the following best describes the parameter p?

Select one:

a. The proportion of all college students who believe in a higher power.b. The proportion of all college students who say they are religious.c. The proportion of all college students who say they pray at least once in a while.d. The proportion of all individuals in the population who are college students.

Question 4

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Referring to the above situation, what is the numerical value of the statistic p̂ that estimates p?

Select one:

a. 0.107b. 0.127c. 0.843d. 1.187

Question 5

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The following situation applies to Questions 5-7:
Suppose that half of all college students "drink to get drunk" at least once in a while. That is, p = 0.5. The College Alcohol Study interviews an SRS of 14,941 college students about their drinking habits.

What is the mean of the sampling distribution of p̂?

Select one:

a. 0.0041b. 0.0500c. 0.2500d. 0.5000e. Cannot be determined from information given.

Question 6

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Referring to the above situation, what is the standard deviation of the sampling distribution of p̂?

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a. 0.0041b. 0.0500c. 0.2500d. 0.5000e. Cannot be determined from information given.

Question 7

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What is the probability of getting a sample proportion, p̂, from an SRS of 14,941 college students between 0.49 and 0.51?

Select one:

a. 0.0244b. 0.0073c. 0.7045d. 0.9854e. 0.9927

Question 8

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In the 2004 election in Utah, 66% of all Utah voters voted for Amendment 3, the marriage amendment. Suppose a Statistics major decided to predict the theoretical sampling distribution of p̂ for samples of size 100. What is the mean of this sampling distribution of p̂?

Select one:

a. The mean equals p̂ which is 66%.b. The mean equals p = 0.66.c. The mean will equal p, but we don’t know what the value of p is.

Question 9

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What would happen to the mean of the sampling distribution of p̂ if the stat major predicted the sampling distribution of p̂ for samples of size 500 instead of size 100?

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a. The mean would decrease.b. The mean would stay the same.c. The mean would increase.

Question 10

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What would happen to the standard deviation of the sampling distribution of p̂ if samples of size 500 were taken instead of samples of size 100?

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a. The standard deviation would be smaller.b. The standard deviation would stay the same.c. The standard deviation would be larger.

Question 11

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What would happen to the shape of the sampling distribution of p̂ if samples of size 500 were taken instead of samples of size 100?

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a. The shape would stay the same.b. The shape would be closer to Normal.c. The shape would be farther from Normal.

Question 12

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True or false: As sample size increases, the standard deviation of the sampling distribution of p̂ also increases.

Select one:

a. Trueb. False

Question 13

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If the population proportion is p = 0.06, will the shape of the sampling distribution of p̂ predicted for random samples of size 100 be approximately Normal?

Select one:

a. Yesb. No

Question 14

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In the 2004 Utah election, the proportion of voters for Initiative 1 was 45% whereas the proportion of voters for Amendment 3 was 77%. Suppose a sampling distribution for p̂ was predicted for the proportion of voters favoring Initiative 1 from samples of size 100. Further, suppose that a sampling distribution for p̂ was predicted for the proportion of voters favoring Amendment 3 also for samples of size 100. How do their shapes compare?

Select one:

a. The sampling distribution for the sample proportion favoring Initiative 1 will be closer to Normal than the sampling distribution for the proportion favoring Amendment 3.b. The sampling distribution for the sample proportion favoring Amendment 3 will be closer to Normal than the sampling distribution for the proportion favoring Initiative 1.c. The shapes of both sampling distributions will be exactly Normal.

Question 15

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A local television station conducts a call-in poll about a proposed city tax increase to buy park areas and protect them from development. Of the 2372 calls, 1921 support the proposal. We can't use these data as the basis for inference about the proportion of all citizens who support the tax increase. Why not?

Select one:

a. The number of people participated in the poll was too small.b. The proportion 1921/2375 = 0.809 is too large to be statistically significant.c. This call-in poll cannot be considered an SRS of the population (“all citizens”).d. The respondents only had two options: either they support or they oppose the proposal. Thus, the proportion who support the proposal should be close to 0.5.