# EBook Problems Estim Proportion

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## Contents |

## EBook Problems Set - Estimating a Population Proportion

### Problem 1

A 1996 poll of 1,200 African American adults found that 708 think that the American dream has become impossible to achieve. The New Yorker magazine editors want to estimate the proportion of all African American adults who feel this way. Which of the following is an approximate 90% confidence interval for the proportion of all African American adults who feel this way?

- Choose one answer.

*(a) (.56, .62)*

*(b) (.57, .61)*

*(c) Can't be calculated because the population size is too small.*

*(d) Can't be calculated because the sample size is too small.*

### Problem 2

True or False: In a well-designed sample survey like the Current Population Survey, the observed sample percentage (e.g, percentage unemployed) is equal to the population percentage. Thus, it is appropriate to just report the sample percentage, without any measure of accuracy (i.e. without the margin of error).

- Choose one answer.

*(a) True*

*(b) False*

### Problem 3

The BBC news does a story and at one point the reporter says: "A polling agency reports that the percentage of the American public who agree we should spend more money on the mental health of the war veterans is 42% +/- 3%."

- Choose one answer.

*(a) The probability that the American public agree that we should spend more money on the mental health of the war veterans is between 39% to 42%.*

*(b) The percentage of the American public who agree that we should spend more money on the mental health of the war veterans is between 39% to 45%.*

*(c) We are 95% confident that the percentage of the American public who agree that we should spend more money on the mental health of the war veterans is between 39% to 45%.*

*(d) The percentage of the American public who agree that we should spend more money on the mental health of the war veterans is 42%.*

### Problem 4

A school district is worried that too many students are failing the high school exit exam. In a random sample of 60 high school students, there are 9 students who fail the exit exam. Administrators want to estimate the percentage of the students who fail with a margin of error of 3% and confidence level of 90%. How many students should they sample for a thorough investigation of the problem?

- Choose one answer.

*(a) 278*

*(b) 544*

*(c) 383*

*(d) 233*

### Problem 5

A major newspaper wants to hire a polling agency to predict who will be the next governor. Agency A proposes to do the job with a random sample of 5000 voters at a cost of $50K (K = one thousand). Agency B proposes to do the job with a random sample of 7500 voters at a cost of $75K. Assume both agencies find the percentage of voters to be 40% and both use the normal model to calculate the 95% interval. Which agency will you hire? Hint: Compare the margin of error for the two agencies and the relative costs before making your decision.

- Choose one answer.

*(a) I will hire B.*

*(b) I have no preference.*

*(c) I need more information to decide who to hire.*

*(d) I will hire A.*

### Problem 6

Suppose that the proportion of the adult population who jog is 0.15. What is the probability that the proportion of joggers in a random sample of size n =200 lies between 0.13 and 0.17?

- Choose one answer.

*(a) 0.5762 approximately*

*(b) 0.8125 approximately*

*(c) 0.2345 approximately*

*(d) 0.1234 approximately*

### Problem 7

An investigator made a careful sample survey to estimate the prevalence of drug use at UCLA. Two assistants were stationed in front of Ackerman Union and instructed to interview all students who passed through at specified times. As it turned out, 39% of 369 students interviewed said they had used ecstasy at least once. Which of the following statements is correct?

- Choose one answer.

*(a) Since this is a sample of convenience, the confidence interval does not say anything about the prevalence of drug use at UCLA*

*(b) The population proportion is within 1.96 standard deviations of the sample proportion in 95% of the surveys.*

*(c) Since the sample was selected from Ackerman Union, the confidence interval only applies to the South campus.*

*(d) If we drew 100 samples from the population of UCLA students, 95% of the different confidence intervals we would obtain would contain the true population proportion.*

### Problem 8

A survey is carried out at a university to estimate the percentage of undergraduates living at home during the current term. What is the population? What is the parameter?

- Choose one answer.

*(a) Population: undergraduates in this university. Parameter: percentage of undergraduates in this university living at home during the current term.*

*(b) Population: undergraduates in US universities. Parameter: percentage of all university students living at home during current term*

*(c) Population: undergraduates in US universities. Parameter: percentage of this university students living at home during current term*

*(d) Population: adults in the US. Parameter: Parameter: percentage of undergraduates in this university living at home during the current term.*

### Problem 9

A recent Gallup Poll found that 23% of senior citizens exercise at least 3 times a week. The number 23% is

- Choose one answer.

*(a) The percentage of all senior citizens who exercise in the population*

*(b) A parameter*

*(c) A sample*

*(d) An estimate of the percentage of all senior citizens who exercise in the population*

### Problem 10

Market researchers are interested in determining the true proportion of college students who use their ATM each week. Suppose they take 100 random samples of 40 college students and count those who use their ATM this week. Describe the distribution of proportions selected from each of these samples.

- Choose one answer.

*(a) The distribution of sample proportions is Binomial*

*(b) The distribution of sample proportions is nearly normal.*

*(c) The distribution of sample proportions is skewed to the left or low end.*

*(d) The distribution of sample proportions is skewed to the right or high end.*

### Problem 11

Suppose that you and everyone else in a large stat class each selects a random sample of 50 Skittles candies, counts the greens, and computes the proportion of greens in their sample. Which of the following statements is true?

- Choose one answer.

*(a) Most of the class will have sample proportions within two deviations of the proportion of green Skittles in the population.*

*(b) The proportion of green Skittles in our sample will be equal to the proportion of Skittles in the population since the sample size is large.*

*(c) The proportion of green Skittles will always be within two deviations of our sample proportion.*

### Problem 12

Records at a large university (not UCLA, of course) indicate that 20% of all freshmen are placed on academic probation at the end of the first semester. A random sample of 100 freshmen found that 25% of them were placed on probation. The results of the sample:

- Choose one answer.

*(a) are surprising since it indicates that 5% more of these freshmen were placed on probation than expected*

*(b) are surprising since the standard deviation of the sampling distribution is 0.4%.*

*(c) are biased since an increase of 5% could not happen without injecting bias into the sample.*

*(d) are not surprising since the standard deviation of the sampling distribution is 4%.*

*(e) are surprising since SAT scores have increased over the past years*

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