Free Printable Estimating a Parameter

1.

According to DuPont 2012 Global Automotive Color Popularity Report, 23% of all cars manufactured in 2012 were white. In a random sample of 100 cars parked in long-term parking at Philadelphia International Airport, 19% of the cars were white. Which of the following statements is true?

a)

19% and 23% are parameters, 100 is a statistic.

b)

23% is a parameter, 19% is a statistic

c)

23% is a statistic, 19% is a parameter

d)

19%, 23%, and 100 are all statistics

2.

In a recent Gallup poll of randomly selected US adults, 75% said they would vote for a law that imposed term limits on members of the US Congress. The poll's margin of error was 4 percentage points at the 95% confidence level. This means that

a)

the poll used a method that gets an answer within 4 percentage points of the truth about the population 95% of the time.

b)

if Gallup takes another poll on this issue, the results of the second poll will lie between 71% and 79%.

c)

there is convincing evidence that more than 79% of all US adults would vote for term limits.

d)

Gallup can be 95% confident that between 71% and 79% of the adults in the sample would vote for term limits.

3.

A 95% confidence interval for p, the proportion of all shoppers at a large grocery store who purchase cookies, is 0.236 to 0.282. The point estimate and margin of error for this interval are:

a)

point estimate = 0.236; margin of error = 0.282

b)

point estimate = 0.236; margin of error = 0.046

c)

point estimate = 0.259; margin of error = 0.046

d)

point estimate = 0.259; margin of error = 0.023

4.

A quality control manager at a manufacturing plant wants to estimate the mean length of metal rods produced by a certain machine. The manager is deciding between a 95% confidence level and a 99% confidence level. Compared to a 95% CI, a 99% CI will be

a)

narrower and would involve a larger risk of being incorrect.

b)

wider and would involve a smaller risk of being incorrect.

c)

narrower and would involve a smaller risk of being incorrect.

d)

wider and would involve a larger risk of being incorrect.

5.

Isabel selects a simple random sample of 28 seniors at her school and finds that 20 of them are planning to participate in the school's annual capture-the-flag game. She wants to construct a CI for p = the proportion of all seniors who plan to participate in the game, but she realizes she hasn't met all the conditions for constructing the interval. Which condition for this procedure has she failed to meet?

a)

n ≥ 30

b)

np̂ ≥ 10

c)

n(1 - p̂) ≥ 10

d)

The population must be approximately normal.

6.

Most people can roll their tongues, but some can't. Suppose we are interesting in determining what proportion of people in a certain population can roll their tongues. We test a random sample of 80 people from this population and find that 64 can roll their tongues. The margin of error for a 95%CI for the true proportion of tongue rollers in this population is closest to

a)

0.004

b)

0.045

c)

0.088

d)

0.176

7.

Many TV viewers express doubts about the validity of certain commercials. In an attempt to answer their critics, Times Group USA wishes to estimate the proportion of consumers who believe what is shown in Timex TV commercials. Let p represent the true proportion of consumers who believe what is shown in Timex TV commercials. Which of the following is the smallest number of consumers that Timex can survey to guarantee a margin of error of 0.05 or less at the 99% confidence level?

a)

600

b)

650

c)

700

d)

750

8.

In checking conditions for constructing CIs for a population mean, it's important to plot the distribution of sample data. Each dotplot shoss the distribution of a sample from a different population. For which of the three samples would it be safe to construct a one-sample t interval for the population mean?

a)

Sample X only

b)

Sample Y only

c)

Sample Y and Z

d)

None of the samples

9.

You want to calculate a 98% CI for a population mean from a sample of size n = 18. What is the appropriate critical value t*?

a)

2.110

b)

2.224

c)

2.552

d)

2.567

10.

A sample size of n = 64 is drawn from a population whose standard deviation is σ = 5.6.

Find the margin of error for a 99% confidence interval for µ.

a)

1.799

b)

1.798

c)

1.803

11.

A large sample has mean of 7.1 and Standard Error of 2.3.

Construct a 90% Confidence Interval for the population mean µ (to two decimal places).

a)

(3.32, 10.88)

b)

(3.8, 7.1)

c)

(3.3, 10.9)

d)

(3.3165, 10.8835)

12.

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.

What is the point estimate?

a)

75

b)

105.2

c)

10

d)

0.90

13.

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.

Find the critical value.

a)

0.90

b)

1.155

c)

1.645

d)

±1.645

14.

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.

Find the Standard Error.

a)

75

b)

10

c)

105.2

d)

1.155

15.

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.

Find the Margin of Error to two decimal places.

a)

1.90

b)

1.89

c)

1.899

d)

1.99

16.

The lifetime of a certain type of batter is known to be normally distributed with a standard deviation of 20 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 99% confidence interval for the mean lifetime of this type of battery.

What is the Confidence Interval to one decimal place?

a)

(114.5, 125.6)

b)

(112.8, 127.4)

c)

(112.82, 127.38)

d)

(114.56, 125.64)

17.

If the 95% Confidence Interval for a population mean is (114.56, 125.54), then is it likely that the true population mean µ is greater than 130?

a)

Yes

b)

No

c)

Not enough information

d)

I have no idea what you're asking of me

18.

A population has a standard deviation of σ = 17.3. How large of a sample must be drawn so that a 95% confidence interval for µ will have a Margin of Error equal to 1.4?

a)

586.6

b)

587

c)

586

d)

585

19.

A person selects a random sample of 15 credit cards and determines the annual interest rate, in percent, of each one. The sample mean is 12.42 with a sample standard deviation of 1.3. It is desired to construct a 90% Confidence Interval.

Find the Standard Error to three decimal places.

a)

0.336

b)

0.33566

c)

13.156

d)

0.087

20.

True or False:

The more confident you want to be, the smaller your confidence interval will be.

a)

True

b)

False

21.

True or False:

The larger your confidence interval is, the more sure (higher confidence level) you can be.

a)

True

b)

False

Estimating a Parameter

Total questions: 21

Worksheet time: 39mins

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