Stats Final

Stocks have PE ratios that have a normal distribution with mean 15 and standard deviation 5. 10% of the stocks have a PE ratio less than what value?

8.6

Suppose Bob questions whether cereal boxes are being filled correctly, and he believes they are being underfilled. He collects his data, finds his test statistic and p-value, and ends up failing to reject Ho. He didn't have enough evidence to say the cereal boxes were being underfilled. What Type of error could Bob have made?

Type 2

Which of the following requires independence? Mean (X-Y)= Mean X - Mean Y Var (X-Y) = Var(X) + Var(Y) SD(X+Y) = Sqrt(Variance of (X+Y)) All of these choices require independence

Var (X-Y) = Var(X) + Var(Y)

You want to estimate the average time to do a task for your employees in the mailroom. You take a sample of 10 employees and time them doing this task. The average time is 34 seconds with sample standard deviation of 5.2 seconds. What is the margin of error?

3.72

Bob guesses randomly on a 20 question multiple choice test where there are 4 possible answers for each question. What is the variance of the number of answers Bob gets right?

3.75

Suppose a pizza place claims their pizzas are delivered in 30 minutes and Bob believes it's more than that. Bob samples 49 pizza delivery times at random and gets an average of 35 and sample standard deviation 10 min. What is the value of u0 in this problem? (That's mu sub 0).

30

X is a normal random variable with mean 10 and standard deviation 3 Y is a normal random variable with mean 20 and standard deviation 4 X and Y are independent. Find the mean and standard deviation of X - Y

-10 and 5

Suppose you want to estimate the average price of gas in Ohio and your 95% confidence interval was (1.20, 1.50). How confident are you that the SAMPLE MEAN is in this interval?

100%

You want to estimate the average amount of revenue from all the bank branches of your company in the U.S. You want the margin of error to be no more than 1000. Assume the standard deviation is 30,000. How many branches should be sampled?

3458

Suppose X has a normal distribution with mean 80 and standard deviation 5. Then about 95% of the values must lie between what two numbers?

70 and 90

Exam scores have a mean of 70 and standard deviation 10. The professor wants to give everyone a 10% curve added to their score. What is the new mean?

77

Suppose you are doing a hypothesis test Ho: u = 30 vs Ha: u > 30 with n = 10. The sample average is 34 seconds with sample standard deviation of 5.2 seconds and your test statistic is 2.43. Where is your p-value?

Between .025 and .01

When you take all possible sample means from all possible samples of size n from a population and put them all together, what do you have?

Sampling distribution

Let X be a continuous random variable from 0 to 2 with f(x) = x/2. What is the mean of X?

Some number between 1 and 2.

A confidence interval gets wider when you don't know the population standard deviation because you have to use t instead of Z.

True

Coefficient of determination works for any type of relationship.

True

If you are counting the number of RED M&Ms in a bag you have a binomial distribution.

True

Let X be a continuous random variable with f(x) = x/2 on 0 to 2. True or false? The median of X is the square root of 2.

True

The t-distribution looks more and more like the Z distribution as n gets larger and larger.

True

last year the average time to do a task for your employees was 30 seconds, and you are afraid it's now more than that. You take a sample of 10 employees and time them doing this task. The average time is 34 seconds with sample standard deviation of 5.2 seconds. True or false: Your test statistic is 2.43.

True

What happens to the standard error of X-bar as n increases to infinity?

it goes to 0

The best fitting regression line has an SSE that is _____________ any other possible line that goes through the data points.

less than

What conditions need to be checked before you use Z to solve a binomial problem with a large n?

np and n(1-p) at least 10

If a data point has a negative residual, where is the point compared to the line?

point is below the line

Let X have a normal distribution with mean 70 and standard deviation 5. Let X-bar be the mean of 20 values chosen at random from it. What is bigger, P(X > 75) or P(X-bar>75)?

prob for X is larger

Which distribution has a larger standard deviation, the Z or the t?

t

Suppose 90% of students are at home over the summer. You randomly select 2 students. What's the chance that exactly one of them is at home over the summer?

.09

Suppose Bob conducted a hypothesis test for the mean where Ho: mu = 20 and Ha: mu < 20, and found a test statistic of -1.28. What is his p-value?

.1003

Research says that 80% of companies start making a profit after 3 years. You take a random sample of 100 companies. what's the chance that at most 75 of them make a profit after 3 years?

.1056

What is the probability that Z is at least 1.25?

.1056

Suppose you want to estimate the average price of gas in Ohio and your 95% confidence interval was (1.20, 1.50). What is the margin of error for this confidence interval?

.15

Suppose Bob conducted a hypothesis test for the mean where Ho: mu = 20 and Ha: mu not equal to 20, and found a test statistic of -1.28. What is his p-value?

.2006

Stocks have PE ratios that have a normal distribution with mean 15 and standard deviation 5. What is the probability that a stock has a PE ratio of at most 22?

.9192

Suppose X is binomial with n = 5 and p = .3. Find the probability that X is at most 4.

.9976

If you did a t-test and got a p-value between .03 and .07, what do you conclude?

Fail to reject Ho

If you count the number of M&Ms of each color you have a binomial distribution.

False

On a regression line, you can find a residual for any value anywhere on the entire line. True or false?

False

P(Z < -1) = 1- P(Z > 1) True or False?

False

Suppose X is a continuous random variable. Then f(x) must be between 0 and 1 for all values of X.

False

The NORMAL PROBABILITY PLOT should look like a bell-shaped curve if the data have a normal distribution.

False

True or False? Z and t can both take on negative numbers.

Z and t can both be negative

Let X be a continuous random variable with f(x) = x/2 for X from 0 to b. Find the value of b.

b = 2

If X is a binomial random variable then X is also a __________________ random variable.

discrete finite

Suppose X = study time and Y = exam score. Suppose the best fitting regression line is Y = 30 + 10X. Interpret the slope.

As X increases by 1, Y increases by 10

Let X be uniform on the interval 0 to 10. What is f(5) and what is P(X = 5)?

1/10, 0

Suppose f(x) = kx for X from 0 to 2. Find the value of k.

1/2

Suppose X is uniform on the interval 0 to 20. What is f(x)?

1/20

Bob guesses randomly on a 20 question multiple choice test where there are 4 possible answers for each question. This is a binomial distribution where Yes = got it right, and No = got it wrong. What is the value of p?

1/4

You want to estimate the average time to do a task for your employees in the mailroom. You take a sample of 10 employees and time them doing this task. The average time is 34 seconds with sample standard deviation of 5.2 seconds. What is the value of t that goes in the confidence interval?

2.2622

Suppose a pizza place claims their pizzas are delivered in 30 minutes and Bob believes it's more than that. Bob samples 49 pizza delivery times at random and gets an average of 35 and sample standard deviation 10 min. What is the test statistic?

3.5

Suppose a pizza place claims their pizzas are delivered in 30 minutes and Bob believes it's more than that. Bob samples 49 pizza delivery times at random and gets an average of 35 and sample standard deviation 10 min. What are the hypotheses in this problem?

Ho: u = 30 and Ha: u > 30

What is the term for making predictions outside the range of the data values for X?

extrapolation

Suppose Bob conducted a hypothesis test for the mean where Ho: u = 80 vs Ha: u > 80 and he gets a p-value of .06. What does Bob decide to do about Ho?

fail to reject Ho

What element of X-bar is addressed by the Central limit theorem, the shape, mean, or standard deviation?

shape only