Jeopardy! Confidence Intervals Review

Sample Size It

100

When doing a confindence interval for difference of means, and sigma is unknown, what critical value do you use?

t*

200

When can we use n = p(1-p)(Z*/ME)^2 to find sample size?

When we have a prelim. estimate for p.

300

The average heights of a random sample of 400 people from a city is 1.75 meters. It is known that the heights of the population are random variables that follow a normal distribution with a standard deviation of 0.4 meters. With a confidence level of 90%, what would the minimum sample size need to be in order for the true mean of the heights to be within .02 m from the sample mean?

1083

400

What sample size should be taken to estimate p within .05 at a 95% level?

385

500

From previos studies pro football players weights have shown a standard deviation of 20 lbs. To ensure a confidence level of 90%, what would the minimum sample size need to be in order for the true mean of weights to be within 2 lbs. from the sample mean?

271

"Critical" Information

100

What happens to the width of the intervals when you increase your confidence level?

they get wider

200

What happens to the width of the intervals when you increase ME?

wider

300

For a sample size of 20, what are the degrees of freedom?

19

400

For 2 samples, one of size of 11 and one of size 13, what are the degrees of freedom? and the corresponding t* for a 85% level?

22 and 1.492

500

ERROR

ERROR

Solo Sample Confidence

100

For a one-sample proportion confidence interval, the middle value of the interval is equal to what?

p-hat

200

What is the formula for a one-sample proportion confidence interval?

p-hat +/- z*sqrt(p-hat*q-hat/n)

300

What does n*p-hat and n*q-hat have to be greater than?

10

400

Which of the following statements is true? I. The margin error (ME) is computed solely from sample attributes and a critical value II. The sample standard deviation is x-bar. III. The standard deviation is a measure of central tendency. (A) I only (B) II only (C) III only (D) All of the above. (E) None of the above.

The correct answer is (A)

500

Suppose we want to estimate the average weight of an adult male in Dekalb County, Georgia. We draw a random sample of 1,000 men from a population of 1,000,000 men and weigh them. We find that the average man in our sample weighs 180 pounds, and the standard deviation of the sample is 30 pounds. What is the 95% confidence interval? (A) 180 +/- 1.86 (B) 180 +/- 3.0 (C) 180 +/- 5.88 (D) 180 +/- 30 (E) None of the above

The correct answer is (A)

Confidence Interval Mix 'n Match

100

2 Sample Confidence Interval for proportions estimates the difference between what two values?

p1 and p2

200

The average heights of a random sample of 400 people from a city is 1.75 meters with a standard deviation of 0.4 meters. The average heights of a second random sample of 500 people from a city is 1.82 meters with a standard deviation of 0.5 meters. Compute a confidence interval of 90%, for the difference of the two means.

(-.012, -.02)

300

The average heights of a random sample of 400 people from a city is 1.75 m. It is known that the heights of the population are random variables that follow a normal distribution with a standard deviation of 0.4 m. Determine the interval of 95% confidence for the average heights of the population.

n = 400 x = 1.75 σ = 0.4 c = 0.95 z* = 1.96 (1.75 ± 1.96 · 0.4/20 ) → (1.7108, 1.7892)

400

What happens to the WIDTH of the intervals when you INCREASE your sample size?

The intervals become narrower.

500

Suppose that you want to find out the average weight of all players on the football team at Landers College. You are able to select ten players at random and weigh them. The mean weight of the sample of players is 198, so that number is your mean estimate. The population standard deviation is σ = 11.50. Construct a 90 percent confidence interval for the population weight, if you presume the players' weights are normally distributed.

We are 90 percent confident that the true population mean of football player weights is between 192 and 204 pounds.

Pick Me!

100

Mr. Ambrosio holds a passport to another country. What country is it?

Ireland

200

The father of this influential Newark politician was the Poet Laureate of New Jersey

Ras Baraka (His father is Amina Baraka was the Poet Laureate of New Jersey)

300

This city is home to the largest collection of cherry blossom trees in the United States 

Newark, NJ

400

Which of the following is NOT true about constructing confidence intervals? (A) The value of the standard error is a function of the sample statistics. (B) The center of the confidence interval is the population parameter. (C) One of the values that affects the width of a confidence interval is the sample size. (D) If the value of the population parameter is known, it is irrelevant to calculate a confidence interval for it. (E) The value of the level of confidence will affect the width of a confidence interval.

(B)

500

If the 95% confidence interval of the proportion of a population is .35 ± .025, which of the following is NOT correct? (A) If the sample size were to increase, the width of the interval would decrease. (B) An increase in confidence level generally results in an increase in the width of the confidence interval. (C) This confidence interval could have been calculated after either a sample or a census was conducted. (D) If one would like a smaller confidence interval, one could increase sample size or decrease the confidence level. (E) All of these are correct.

(C)