Stats final
tn-1 is a value on the t distribution with ______________________________ n-1.
Degrees of Freedom
If your p-value is .11, and the significance level is .05, what do you conclude?
Fail to reject Ho
A Type 2 error is described as a false alarm.
False
A confidence interval is narrower if you use t than if you use Z. (Assume all else is the same.)
False
Failing to reject Ho and Accepting Ho are both appropriate conclusions that mean the same thing.
False
If X is binomial with n = 5 and p = 0.05, the chance that X is at least 1 is 0.7738
False
If you reject Ho in a hypothesis test for the mean, the value of uo is guaranteed not to be in the corresponding confidence interval. (Assume Ha is , alpha = .05, confidence level = 95%)
False
If your test statistic is negative, so is your p-value.
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 significance level is the same as a Type 2 error.
False
The t distribution is taller and thinner (more concentrated around the mean) than the Z distribution.
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.
Bottles of cream have a normal distribution with mean 8 ounces. You would stop the process if the containers were being filled incorrectly. What is your alternative hypothesis?
Ha: u not equal to 8
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
What is the name for the cutoff value that lets you decide between rejecting Ho and failing to reject Ho with your p-value?
Significance Level
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
When you take the given information and form a Z-score in a hypothesis test for the mean, what is the special name of that result?
Test statistic
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 Ha is not equals, you have to double the probability of being beyond your test statistic to get your p-value.
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
Suppose n = 10 and you want the value of t to put in your 95% confidence interval for the mean, where you don't know the population standard deviation. The value of t that you find on the t-table in this case is 2.2622.
True
The 80th percentile of the standard normal (Z) distribution is .84.
True
The larger n is, the closer the t distribution looks to the Z distribution.
True
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
You must use a t instead of a Z in your confidence interval formula for a mean when you don't know the value of sigma. (Assume you have a normal distribution.)
True
If you reject Ho, which type of error could you be making?
Type 1 Error
Which of the following describes the relationship between parameters and statistics?
We use statistics to estimate or test parameters
Suppose a 95% confidence interval for the mean is (10, 12) when you know the value of the population standard deviation (sigma). If you HAD NOT known the value of sigma, would your confidence interval have been wider, narrower, or the same?
Wider
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
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
Suppose someone reports that the average age of all Pokemon players is 13. You believe it's higher than that because your statistics professor plays Pokemon. You decide to challenge the claim. Do you use a confidence interval or a hypothesis test?
hypothesis test
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 X has a normal distribution and you run a hypothesis test with Ho: u = 8 and Ha: u > 8. You collect a random sample of n = 11 values, and you find your test statistic is t = 2.50. What is your decision?
reject Ho
If you don't know the population standard deviation, what do you use as a substitute in your test statistic?
s
A continuous random variable has a(n) __________________________ number of possible values.
uncountable infinite
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
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
Bottles of cream have a normal distribution with mean 8 ounces. You would stop the process if the containers were being filled incorrectly. Your sample of 30 containers has an average weight of 7.7 ounces. Assume the standard deviation is .8. What is your test statistic?
-2.05
Suppose X has a normal distribution and you run a hypothesis test with Ho: u = 8 and Ha: u > 8. You collect a random sample of n = 11 values, and you find your test statistic is t = 2.50. What two values does the p-value lie between on the t-table?
.01 < p value < .025
Bob's alternative hypothesis is Ha: u > 8 and his test statistic is 1.75. What is Bob's p-value?
.0401
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
In testing the hypotheses 800 vs Ho: µ≠800, if the value of the test statistic equals 1.75, then the p-value is:
0.0802
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
Suppose you want to estimate the average age of all Pokemon players. Would you use a confidence interval or a hypothesis test?
A confidence interval
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
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.
