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"Critical" Information
Solo Sample Confidence
Confidence Interval Mix 'n Match
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100
When doing a confindence interval for difference of means, and the population standard deviation is unknown, what critical value do you use?
t*
100
What happens to the width of the intervals when you increase your confidence level?
they get wider
100
For a one-sample proportion confidence interval, the sample proportion is what?
p-hat
100
The best point estimate of the population mean is the...
sample mean
100
If the 90% confidence interval of the mean of a population is given by 45 ± 3.24, which of the following is correct? (A) We are 90% confident that the true mean is in the interval. (B) There is a 90% probability that the sample mean is in the interval. (C) If 100 samples of the same size are taken from the population, then approximately 90 of them will contain the true mean. (D) There is a 90% probability that a data value, chosen at random, will fall in this interval. (E) None of these is correct.
(C) or (A)
200
How do we find the minimum sample size if we are given the population standard deviation?
n=((z*)(sigma)/E)^2
200
What happens to the width of the intervals when you increase the margin of error?
wider
200
What is the formula for a one-sample proportion confidence interval?
p-hat +/- z*sqrt(p-hat*q-hat/n)
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. Which critical value would you use for this confidence interval?
t*
200
The critical value for a 99% confidence interval for p is: (A) 1 (B) 1.96 (C) 2 (D) 2.78 (E) 2.58
(E)
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
300
For a sample size of 20, what are the degrees of freedom?
19
300
How do you find q^hat?
1-p^
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)
300
What is the difference between a parameter and a statistic?
parameter comes from population

statistic comes form sample

400
What sample size should be taken to estimate p within .05 at a 95% level if the population standard deviation is .25?
97
400
For a sample of size 13, what are the degrees of freedom? and the corresponding t* for a 95% level?
12 and 2.179
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)
400
What happens to the WIDTH of the intervals when you INCREASE your sample size?
The intervals become narrower.
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
From previous 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
500
If sample size is increased, what happens to the width of the confidence interval?
wider
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)
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.
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)