Stats final

The personnel department keeps records on all employees in a company. Here is the information they keep in one of their data files: Employee identification number Last name First name Middle initial Department Number of years with the company Salary ($) Education Level (high school, some college, or college degree) Age (years) Which of the following combinations of variables would be appropriate to examine with a scatterplot?

Age and Salary

The mean cost of a box of cheerios oat crunch is $4. If the price increases by 10% what is the new mean

$4.40

Suppose you have 4 data sets whose scatterplots all show possible linear relationships. The four data sets have correlations of -0.10, 0.25, -0.90, and 0.80, respectively. . Which of the correlations shows the strongest linear relationship?

-0.90

Where is the 10th percentile of the Z distribution?

-1.28

x 1 2 p(x) .5 .5 What is the variance of X

.25

The mean cost of a box of Cheerios Oat Crunch is $4.00 and the variance is .35. If the price increases by 25 cents a box, what is the new variance?

.35

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

.7

Let f(x) = 3x^2for 0 < x < 1. What is the median of X? Choose the closest answer!

.8

X is a normally distributed random variable with mean 50 and standard deviation 5. What is the probability that X will be less than 55?

.841

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

0

What is the probability that a normally distributed random variable X is greater than 85 if μX= 75 and σX= 4? CHOOSE THE CLOSEST ANSWER.

0.0006

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

0.019

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 less than 2?

0.0463

x p(x) 1 .1 2 .3 3 .6 What is the probability that x is at least 2

0.90

Suppose X = exam score and X has a normal distribution with mean 80 and standard deviation 5. Bob scored at the 90th percentile. What is Bob's Z-value (aka Z-score)?

1.28

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

If your confidence interval is 95%, what is the value of Z that goes into the confidence interval formula?

1.96

Suppose X has a uniform distribution on the interval [0, 10]. What is f(x)?

1/10

Let f(x) = kx where x is between 0 and 2. What is the value of k that makes this a legitimate density function?

1/2

f(x) = 1/2 between 0 and 2. What is the probability that X is between 1 and 3?

1/2

Let f(x) = 3x^2for 0 < x < 1. What is P(X < 1/2)? Choose the closest answer!

1/8

Let X = time waiting in line at a restaurant to get a seat. Mean of X = 20 min, Variance of X = 25 Let Y = time waiting for your food to arrive. Mean of X = 30 min, Variance of Y = 36 X and Y are correlated and the correlation is 0.80. What is the variance of the TOTAL TIME waiting?

109

Bob wants a 95% confidence interval for the population mean. Previous research shows the population standard deviation is 8. He wants his margin of error to be no more than 4. What should his sample size be?

16

If the variance of X is 10, what is the variance of 4X + 20?

160

Suppose X has a normal distribution with mean 80 and standard deviation 5. How many standard deviations above or below the mean is 70?

2 Standard Deviations below the mean

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

2.25

x 1 2 p(x) .5 .5 y 1 2 p(y) .9 .1 What is the mean of x + y

2.6

Let f(x) = 3x^2for 0 < x < 1. What is the mean of X? Choose the closest answer!

3/4

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

4/9

Bob makes a 95% confidence interval with a random sample of 100 and his margin of error is plus or minus 18. In order to cut the margin of error in half next time, what should Bob's sample size be? (Hint: You CAN determine the answer without knowing the standard deviation.)

400

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

Suppose X = number of women in a sample of size 100 from a population that has 80% women and 20% men. X has an approximate normal distribution with mean _____ and standard deviation ______.

80, 4

Suppose X has a normal distribution with mean 80 and standard deviation 5. What is the 90th percentile of X?

86.4

Your boss gives you the following regression equation. X = square feet and Y = selling price Selling price = 5,240 + 33.80x How do you interpret the slope for this equation

As square feet increases by 1, selling price increases by 33.80

If a residual is negative, then the data point lies _____ the regression line.

Below

Bob is interested in examining the relationship between the number of bedrooms in a home and its selling price. After downloading a valid data set from the internet, he calculates the correlation. The correlation value he calculates is only 0.05. What does Bob conclude?

Bob continues his research because even though there is no linear relationship here, there could be a different relationship.

If X is binomial with n = 5 and p = 0.05, the chance that X is at least 1 is 0.7738

False

Suppose X and Y are independent. Then is the following true or false? theta x+y = thetax +thetay

False

Suppose X is a continuous random variable with the pdf defined as below: f(x) = 1/9x^2, 0 < x < 3. True or false? The median of X is 1.5.

False

Suppose X is a discrete random variable with mean 10 and variance 4, and Y is a discrete random variable with mean 20 and variance 9. We do not know whether X and Y are independent. True/False: We can find the variance of X+Y with only the information we are given.

False

Suppose f(x) = 1/2 where 0 < X < 2. True or false? The median of X is 0.50.

False

Suppose the correlation between X = price of a gallon of gasoline and Y = price of a gallon of milk and r = 0.30 Should we go on and try to make predictions for milk prices using gasoline prices using a straight line

False

Suppose the correlation between two variables X and Y is .8. That means the correlation between Y and X is -.8

False

Suppose the correlation between yards rushing and yards passing is .6. The means the correlation between feet rushing and feed passing is .6 x 12

False

The margin of error increases if the sample size increases.

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

The value of α will change if you get a new data set.

False

True or false? Let X be a continuous random variable. Then f(x) must always lie between 0 and 1.

False

True or false? When you integrate e^−x, you get e^−x.

False

X 1 1/2 2 1/4 3 1/4 True/False: The mean of X is 2.

False

Your boss gives you the following regression equation. X = square feet and Y = selling price Selling price = 5,240 + 33.80x Does it make sense to interpret the Y-int for this equation

False

Which of the following variables has a binomial distribution?

Flipping a coin 10 times and counting the number of heads.

Suppose a pizza place claims it's average pizza delivery time is 10 minutes. Bob makes a 95% confidence interval for the average pizza delivery time for this pizza place and gets (15, 20). What does Bob think about the pizza place's claim?

He disagrees with the claim

Suppose someone claims the average delivery time for U.S. packages to be delivered during December is 2 days. You believe it takes longer than that. You conduct a hypothesis test; what are your hypotheses?

Ho: µ = 2 vs. Ha: µ >2

Your friend claims the average price of a burger in the Columbus Gateway Area is $10.00. You believe it's lower than that. What symbol represents the $10 in this scenario?

Mo

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

Mu with subscript X-bar

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

No

What should the residual plot look like if the regression line fits the data well

No fan shapes, points fall around the horizontal line Y=0, random patterns

Let X = time waiting in line at a restaurant to get a seat in minutes. What are the units of the variance of X? Choose the best answer.

No meaningful units

Which of the following is NOT a continuous random variable?

Number of accidents in one year at an intersection

Which of the following is NOT a discrete random variable?

One that is uncountably infinite

Which of the following terms represents "all possible values of a random variable and how often you expect them to occur?"

Probability distribution

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

Suppose X = number of 1 foot long steps taken in one hour by a person working in a bank. Suppose the mean of X is 300 and the variance is 64. If you change the units from feet to inches, you multiply by 12. What is the new standard deviation?

Sqrt(12^2 x 64)

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

SSE

Sum of Squares for Error

The margin of error is larger if the standard deviation of the population increases (assume all else stays the same.)

True

The p-value will change if you get a new data set.

True

The standard deviation of X is the square root of the variance of X

True

True of False Mx-y = Mx - My

True

True or false. Suppose X and Y are independent Theta^2 x-y = Theta^2x + Theta^2y

True

We are 100% confident that our SAMPLE mean is in every confidence interval we make.

True

With a continuous random variable, P(a < X < b) is the area under the curve f(x) between a and b.

True

Which of the following is NOT a condition of the binomial distribution?

all of these choices are conditions of the binomial

variability

correlation squared r^2

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

A continuous random variable has a(n) __________________________ number of possible values.

uncountable infinite

The 80th percentile of the standard normal (Z) distribution is .84.

True

Everyone at Bob's diner makes $12.00 per hour. Let X = salary of an employee at Bob's diner. What is the mean of X?

$12 per hour

A confidence interval for the mean is known as a range of likely values for the population mean.

The margin of error of a confidence interval gets larger if the confidence level increases (assume all else stays the same.)

Which of the following is true about the mean of the random variable X-bar as n increases?

The mean of X-bar stays the same

The Central Limit theorem tells us important results that pertain to:

The shape (type) of the distribution of X-bar

Which of the following is true about the standard error of the random variable X-bar as n increases?

The standard error of X-bar decreases.

A researcher is trying to predict the linear relationship between January revenue and yearly revenue for her company. The correlation turns out to be 0.60. How does she interpret the correlation

There is a moderate positive linear relationship between January revenue and yearly revenue

A probability density function f(x) tells you how much probability is in the area near x.

True

A researcher is trying to use January temperatures to predict latitude This means January temperature is the x (independent) variable and latitude is the Y (dependent) variable

True

Correlation is affected by outliers

True

Everyone at Bob's diner makes $12.00 per hour. Let X = salary of an employee at Bob's diner. With this information, can you find the variance of X?

True

If X and Y are independent, then True/False: Variance of (X-Y) = Variance of (Y-X)

True

Let f(x) = 3x^2for 0 < x < 1. True or False? P(X < 1/2) = P(X <= 1/2)

True

Suppose Bob makes a 95% confidence interval and his result is (70, 90). True or false: We can tell what Bob's sample mean must have been.

True

Suppose X has a uniform distribution on the interval [0, 10]. True or false, the mean of X is 5.

True

Which of the following describes the relationship between parameters and statistics?

We use statistics to estimate or test parameters

If X does not have a normal distribution, which of the following is true about the shape (distribution) of the random variable X-bar?

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?

X-bar is exactly normal for any n

Suppose: 1. all the points on a scatterplot lie perfectly on a straight line going uphill 2. the mean of X and the mean of Y are both 2 3 the standard deviations of X and Y are exactly the same. Can you find the equation of the best fitting line with this information? (Hint: Think of the '5 number' way of finding the best-fitting line.)

Yes

When you use the normal distribution to find a probability for a binomial random variable, which of the following is true?

You needed np and n(1-p) to be at least 10 and you get an approximate answer.

Suppose the equation y = 3.45 - 2.58x represents a valid regression equation and X can be used to predict Y. From this information, we know that X and Y have _____ correlation

a negative