Stats 1430 Final Exam

When you see "average" in a problem what does it mean?

"Mx" for HT or "x-bar" for probability and CI

When you see "percentage" or a percentage (40%) in a problem what does it mean?

"p" if you see a percent (80%) or "^p" when you see "estimate" or it's a HT

What error do you commit for failing to reject Ho

Type 2 Error

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 error

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

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

1/10, 0

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

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%

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

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 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

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

Fail to reject Ho

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

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

False, because binomial is Yes or No and M&Ms have many colors

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

False, it's a straight line

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

Suppose it is assumed that the weight of yogurt containers have a normal distribution with mean 8 ounces and a standard deviation 1 ounce. You believe the average weight is not 8 ounces. What technique do you use?

Hypothesis test for mean, using Z

If you increase the sample size, what happens to the margin of error in a confidence interval?

It decreases

Suppose Forbes reports the average starting salary for a business graduate is $70,000 and your sample of 100 randomly selected business graduates has an average of $73,000. What label do you use to describe $70,000 in this problem?

Mo

Suppose X and Y are independent. Is it true that the standard deviation of X+Y equals the standard deviation of X plus the standard deviation of Y?

No

What is Type 1 Error?

Rejecting null hypothesis when it is true (false positive)

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.

What error can you commit for rejecting the Ho

Type 1 Error

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

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

True, Z and t can both be negative

Which of the following requires independence?

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

At most

add 0.5 to p-value

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

discrete finite

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 is Type 2 Error?

failing to reject a false null hypothesis (false negative)

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

it goes to 0

A 95% confidence interval for a population proportion is determined to be 0.75 to 0.86. As p-hat approached 1/2 from either direction (above or below), what happens to the margin of error?

it increases

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

less than

If Alternative Hypothesis is not equal to

multiply p-value by 2

Suppose you want to make a condience interval for the average gas price in Ohio. What condition(s) do you need to check, if any, to do this problem?

n>30

When it doesn't say "percentage" in the problem for a confidence interval what condition you use?

n>30

You want to estimate the proportion of all students who will go home for winter break using a confidence interval. Which condition(s) do you need to check in order to do this problem?

n^p>=10 and n(1-^p)>=10

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

How do you calculate residual?

obsy-predy=residual obsy(# you calculate) predy(# they give you in table)

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)?

probability for X is larger because x-bar you divide by the square root of n which makes it smaller

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

shape only

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

t

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

the point is below the line