Statistic and Parameter
What is the difference between a parameter and a statistic?
A parameter refers to the the population and a statistic refers to a sample of individuals in the population.
What is the distribution of values taken by a statistic in all possible samples of the same size from the same population?
A sampling distribution
What happens to the width of the intervals when you increase your confidence level?
The interval gets wider.
Keeping everything else the same, what happens to the WIDTH of the intervals when you INCREASE your sample size?
The interval becomes narrower.
What is a single value estimate for a population parameter?
point estimate
According to Dupont 2007 Global Automotive Color Popularity Report, 19% of all cars manufactured in 2007 were white. In a random sample of 100 cars parked in long-term parking at Philadelphia International Airport, 22% of the cars war white. Define the parameter and statistic for this situation.
19% or .19 is the parameter, .22 or 22% is the statistic.
If the original population is not necessarily normally distributed, how large does a sample have to be in oder for the sampling distribution of the samples mean to be approximately normal?
The sample size must be greater than or equal to 30
For a sample of size 13, what are the degrees of freedom and the corresponding t* for a 85% level?
df = 12, t* = 1.538
If the 90% confidence interval of the mean of a population is given by 45 ± 3.24, which of the following is correct? (A)There is a 90% probability that the true mean is in the interval. (B)There is a 90% probability that the sample mean is in the interval. (C)If 1000 samples of the same size are taken from the population, then approximately 900 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)
Find the sample size: c=0.98, s=10.1, margin of error=3
61.53 (62)
In a study of the effects of acid rain, a random sample of 100 trees from a particular forest is examined. 40% of the trees show some signs of damage. Give the population, and a statistic for the situation.
The population is the set of all trees in the given forest, the statistic is .40 or 40%.
What does the Central Limit Theorem Say?
When the sample size n is large, the sampling distribution of the sample mean x-bar is approximately normal.
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)
Which of the following is NOT true about constructing confidence intervals? (A)The size of the sample affects the width of the interval (B)The center of the confidence interval is the population mean. (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)
Find the margin of error: A company has credit rating scores of a simple random sample of applicants for credit cards: 95% confidence, n=50, mean=677, and standard deviation is known to be 68.
18.85
Which of the following statements are true when taking an SRS from a large population? (A) The sampling distribution of x-bar has standard deviation s=o/square root(n) even if the population is not Normally distributed. (B). the sampling distribution of x-bar is Normal if the population has a Normal distribution. (C). When n is large, the sampling distribution of x-bar is approximately Normal even if the population is not Normally distributed. (D) All of the above.
(D) All of the above
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)
A meteorologist who sampled 13 thunderstorms found that the average speed at which they traveled across a certain state was 15 miles per hour. The standard deviation of the sample was 1.7 miles per hour. Find the 99% confidence interval of the mean.
The weight of at the eggs produced by a certain breed of hen is Normally distributed with a mean of 65 grams and standard deviation of 5 grams. What is the probability that a randomly selected egg weights between 62.5 grams and 68.75 grams?
What is .4649
Suppose you are sampling from a distribution that is strongly skewed left. Which of the following statements about the sampling distribution of the sample mean is true? (A) as the sample size increases, the shape of the sampling distribution gets closer and closer to a Normal distribution. (B) as the sample size increases, the shape of the sampling distribution gets closer and closer to the shape of the population distribution. (C) regardless of the sample size, the shape of the sampling distribution is similar to the shape of the population distribution.
(A) as the sample size increases, the shape of the sampling distribution gets closer and closer to a Normal distribution.
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.
(192, 204)
or
(192.02, 203.98)
An industrial designer wants to determine the average amount of time it takes an adult to assemble an "easy to assemble" toy. A sample of 16 times yielded an average time of 19.92 minutes, with a sample standard deviation of 5.73 minutes. Provide a 95% confidence interval for the mean assembly time.
(16.87, 22.97)
19.92 +/- (2.131)(5.73/sqrt(16))
The weight of the eggs produced by a certain breed of hen is Normally distributed with a mean of 65 grams and standard deviation of 5 grams. Think of carton of such eggs as SRS's of size 12 from the population of all eggs. Calculate the probability that the mean weight of the eggs in a carton falls between 62.5 grams and 68.75 grams..
What is .9535.