Stats Final

If X and Y are random variables, where μ X = 4 , σ X = 8 , μ Y = 7 , and σ Y = 3 what is the mean of 3X-2Y?

-2

Suppose X is the number of cars that a family owns, and that X has the following probability distribution. X 0 1 2 P(x) 0.05 0.39 0.56 Suppose you choose two families at random. What is the chance that family A owns exactly one car and family B owns exactly one car?

0.1521

Use the following probability distribution to find the probability that X is exactly 6. X 3 6 9 P(x) 0.45 0.40 0.15

0.40

The national proportion of adults who are concerned about nutrition is 0.4. You take a random sample of 10 adults and count the number who are concerned about nutrition (call it X). What is the probability that X is at least 2?

0.9537

If X has a continuous uniform distribution on the interval (50, 100), then what is f(75)?

1/50

Suppose X has a continuous random variable with the pdf defined as below: f(x) = (1/9)x^2, 0 < x < 3 What is the mean of X?

2.25

Suppose 20% of Ohio residents support the legalization of marijuana. If you randomly select n people and would like to use the normal approximation to answer questions, what does your sample size have to be, at minimum?

50

Suppose 40% of college students plan to vote in the election. Now suppose we randomly select 200 college students and ask them if they plan to vote. What is the probability that more than 75 of the 200 students sampled plan to vote?

76.4%

The time (X) to complete a standardized exam is approximately normal with a mean of 70 minutes and standard deviation of 10 minutes. How much time should be given to complete the exam so that 80% of the students will complete the exam in the time given?

78.4 minutes

Which of the following describes the relationship between parameters and statistics? A. Statistics and parameters are the same thing B. We use statistics to estimate or test parameters C. We use parameters to estimate or test statistics

B. We use statistics to estimate or test parameters

The Normal distribution is an example of a _________________ Distribution.

Continuous

A p-value for a test statistic in a hypothesis test represents the same value as the sample proportion. True False

False

If X and Y are independent, then Variance of X-Y = Variance of X - Variance of Y

False

Suppose X has a distribution with mean 10 and variance 4, Y has a distribution with mean 20 and variance 9. We do not know whether X and Y are independent. However, we CAN still find the variance of X+Y with only the information we are given.

False

The time to complete a standardized exam is approximately normal with a mean of 70 minutes and a standard deviation of 10 minutes. The percentage of the students which take longer than 80 minutes to complete the exam is 84.13%.

False

Which of the following variables is binomially distributed? Flipping a coin until you get heads Flipping a coin 10 times Both of the above Neither of the above

Flipping a coin 10 times

If you increase n, what happens to the margin of error of your confidence interval for p?

It decreases

What is the symbol we use to represent the mean of the random variable X-bar?

Mu with subscript x-bar

Which of the following is NOT a condition of the binomial distribution? Set number of Trials Two outcomes (yes/no) Independent Trials Fixed Probability p None of the above

None of the above

Is p-hat the sample proportion or the population proportion?

Sample proportion

The set of all possible sample means from all possible samples of size n from the population is known as the:

Sampling distribution of x-bar

A company has developed a new battery, but the average lifetime of all of the batteries it makes is unknown. In order to estimate this average, a sample of 500 batteries is tested and the average lifetime of this sample is found to be 225 hours. The 225 hours is the value of a:

statistic

Suppose X has a normal distribution with mean 10 and standard deviation 2. In order for the Z-score to be equal to 0, then X must be equal to

10

What is the value of ( 5/2 ) ? (Binomial coefficient)

10

If X is a continuous random variable, which of the following conditions does NOT need to be checked to verify that f(x) is a legitimate probability distribution function? A. f(x) must be less than or equal to 1 B. f(x) must be greater than or equal to 0 C. f(x) must integrate to 1 D. All of the above must be checked

A

If X is a binomial random variable with n = 4 and p = 0.18. What is P(X = 3)?

0.019

Use the probability distribution below to find the probability that X is 6 or greater. X 3 6 9 P(x) 0.45 0.40 0.15

0.55

Suppose X has a continuous random variable with the pdf defined as below: f(x) = (1/9)x^2, 0 < x < 3 What is the probability that x is greater than 2?

0.7

If the Z-score is 1.96, and X has a normal distribution with mean 60 and standard deviation 6, what X-value corresponds to this Z-score?

71.76

How large does n generally have to be in order for the Central Limit Theorem to take effect? (Assume X does not have a normal distribution.)

n > 30

Suppose 1063 people out of a random sample of 2054 adults report that they play video games. What is the standard error of p-hat?

0.0110

Suppose X is the number of cars that a family owns, and that X has the following probability distribution. X 0 1 2 P(x) 0.05 0.39 0.56 What is the chance that family owns more than one car?

0.56

If X has a continuous uniform distribution on the interval (50, 100), then what is P(X=75)?

0

X is a normally distributed random variable with mean 50 and standard deviation 5. What is the probability that 2X will be less than 110?

0.841

If X is a random variable with standard deviation 15, then the standard deviation of 2X is 30.

True

Suppose X has a distribution with mean 10 and variance 4, Y has a distribution with mean 20 and variance 9. You can find the mean of X + Y with this information.

True

Where is the 10th percentile of the Z distribution?

-1.28

For a normally distributed variable X with mean 40 and standard deviation 10, what is the probability that X equals exactly 30? In notation, what is P( X = 30 )?

0

Suppose you want to estimate the percentage of all OSU students who will take classes this summer. You take a random sample of 200 OSU students and find that 50 of them will take classes this summer. What is the population in this problem? A. The 200 OSU students who were sampled B. The percentage of all OSU students who will take classes this summer C. All OSU students D. All OSU students who will take classes this summer

C. All OSU students

Which of the following is true about the mean of the random variable X-bar as n increases? A. The mean of X-bar decreases B. Not enough information to tell C. The mean of X-bar stays the same D. The mean of X-bar increases

C. The mean of X-bar stays the same

A binomial random variable is what type of random variable?

Discrete random variable

The number of injuries sustained by an entire football team during a typical college football game is a discrete random variable.

True

For the discrete probability distribution below, the mean of X is 6 units. X 3 6 9 P(x) 0.45 0.40 0.15 True or False

False

If X has a continuous uniform distribution on the interval (0,5), what is the 25th percentile for X?

1.25

If an observation has a z-score of -1.5, how many standard deviations is it above or below the mean?

1.5 standard deviations below the mean

What is the probability that a normally distributed random variable X is greater than 85 if μ X = 75 and σ X = 4?

0.006

Suppose you have a multiple choice test and each question has 4 possible answers. If someone guesses, they would be expected to get 25% of the problems right in the long term. You believe your students did better than just guessing on your exam. If you conducted a hypothesis test for this, what would your hypotheses be? A. Ho: p = 0.25 vs. Ha: p > 0.25 B. Ho: p = 0.25 vs. Ha: p \ne 0.25 C. Ho: p > 0.25 vs. Ha: p = 0.25 D. Ho: p-hat = 0.25 vs. Ha: p-hat \ne 0.25

A.

The Central Limit theorem tells us important results that pertain to: A. The shape (type) of the distribution of X-bar B. The mean of the distribution of X-bar C. All of the above D. The standard error of the distribution of X-bar

A.

If X does not have a normal distribution, which of the following is true about the shape (distribution) of the random variable X-bar? A. X-bar is approximately normal for any n B. X-bar is approximately normal if n > 30 C. X-bar is exactly normal if n > 30 D. X-bar is exactly normal for any n

B. X-bar is approximately normal if n > 30

If X has a normal distribution, which of the following is true about the shape (distribution) of the random variable X-bar? A. X-bar is exactly normal if n > 30 B. X-bar is exactly normal for any n C. X-bar is approximately normal if n > 30 D. X-bar is approximately normal for any n

B. X-bar is exactly normal for any n

The formula for a confidence interval for p involves a Z-value. Why is this? (Assume n is large.) A. Because the original distribution was a normal distribution. B. Because you always use Z in any confidence interval C. Because of the Central Limit Theorem D. All of the above

C. Because of the Central Limit Theorem

Suppose you want to estimate the percentage of all OSU students who will take classes this summer. You take a random sample of 200 OSU students and find that 50 of them will take classes this summer. What is the statistic in this problem? A. The true percentage of all OSU students who will take classes this summer B. 50 C. 200 D. 25%

D. 25%

Which of the following is true about the standard error of the random variable X-bar as n increases? A. The standard error of X-bar increases. B. Not enough information to tell. C. The standard error of X-bar stays the same. D. The standard error of X-bar decreases.

D. The standard error of X-bar decreases

Suppose you want to estimate the percentage of all American families planning a vacation for the summer. Your confidence interval is 30% to 40%. What was your value of p-hat? A. 30% B. 40% C. 10% D. Unknown or none of the above

D. Unknown or none of the above p-hat = 35%

Is the following a legitimate discrete probability distribution? X 3 6 9 P(x) .45 .40 .15 A. Yes, because P(x) is between 0 and 1 for all possible values of X. B. Yes, because P(x) is not the same for each value of X. C. Yes, because the total probability of X sums to 1. D. Yes, because both A and C are true.

D. Yes, because both A and C are true

Suppose your confidence interval for the percentage of all American families planning a vacation for the summer is 30% to 40%. Now suppose the media reported that 50% of American families go on vacation during the summer. Based on your data, would you agree or disagree with them?

Disagree

For the discrete probability distribution below, the variance of X is 5.4 units. X 3 6 9 P(x) 0.45 0.40 0.15 True or False

False

If X has a uniform distribution with f(x)=1/10 we know the values of X MUST go from 0 to 10; they can be nowhere else.

False

If X is a binomial random variable with n = 15 and p = 0.3, we can use the normal approximation.

False

If X is binomial with n = 5 and p = 0.05, the chance that X is at least 1 is 0.6240

False