Stats Final
Suppose you want to investigate a person's salary using their GPA. Suppose the correlationand scatterplot show a strong linear relationship and the best-fitting line is y = $50,000 +$10,000x. Within the range where we can make predictions, what is the expected increase in salary for every 1 point increase in GPA? a. $50,000 b. $10,000 c. Cannot tell without further analysis
b. 10,000
If X is random variable with a standard deviation of 10, then 3X has a standard deviation equal to a. 10 b. 30 c. 90 d. None of the above
b. 30
Suppose the time to serve a customer (X) has a normal distribution with mean 5 minutesand standard deviation 2 minutes. You want to investigate the 5% of customer servicetimes that were the longest. What cutoff point are you looking for? a. 5th percentile for X b. 95th percentile for X
b. 95% percentile
If you do not know the population standard deviation but you want to estimate the average number of hours you study per week, what technique do you use? a. CI for u, involving Z b. CI for u, involving t c. HT for u, involving Z d. HT for u, involving t
b. CI for u, involving t
Suppose your p-value in a hypothesis test is .055. Using the standards from this class what do you conclude? a. Reject Ho b. Fail to reject Ho (since the p-value .055 > significance level of .05.) c. Accept Ho d. Either b or c can be used (we don't say 'accept Ho', we say 'fail to reject Ho'.)
b. Fail to reject Ho
If your p-value is .10, and the significance level is .05, what do you conclude? a. Reject Ho. b. Fail to reject Ho. c. Accept Ho. d. Both b and c are true
b. Fail to reject Ho.
A p-value in hypothesis testing means the same thing as the sample proportion. a. TRUE b. FALSE
b. False
A residual can be calculated anywhere along the regression line, not just where the data points are. a. True b. False
b. False
If Z = .50 that means 50% of the data lie below Z. a. True b. False
b. False
If everyone at your workplace got a 10% raise, the standard deviation of salaries would decrease. a. TRUE b. FALSE
b. False
If someone claims the population mean is 5 and you believe it's greater than 5, you write the following hypotheses: Ho: x bar = 5 and Ha: x bar > 5 a. True b. False (MUST USE population mean μ NOT sample mean)
b. False
R-squared measures the % of points that lie exactly on the regression line. a. True b. False
b. False
Suppose X = the number of rolls needed until you get a 1 on a single die. Then X is a binomial random variable. a. True b. False
b. False
The mean of X+Y = mean of X + mean of Y ONLY when X and Y are independent. a. TRUE b. FALSE
b. False
If X is a continuous random variable and its probability density function is f(x), then we know that the values of f(x) must always lie between 0 and 1. a. True b. False (can be greater than 1)
b. False (can be greater than 1)
If you want to estimate the population mean, which technique do you use? a. Report the mean of your sample b. Find a confidence interval for μ c. Conduct a hypothesis test for μ d. None of the above
b. Find a confidence interval for u
If you have a normal distribution and you want to find the cutoff for the top 30 percent how do you attack the problem? a. Find the 30th percentile b. Find the 70th percentile c. Find the probability that Z < .70 d. Both b and c are correct
b. Find the 70th percentile
If you increase the sample size, what happens to the margin of error in a confidence interval? a. It increases b. It decreases c. It stays the same
b. It decreases
How does the t distribution differ from the Z distribution? a. It has a smaller standard deviation and hence thinner tails than the Z distribution. b. It has a larger standard deviation and hence thicker tails than the Z distribution. c. The t and Z distributions are no different.
b. It has a larger standard deviation and hence thicker tails than the Z distribution.
If you switch X and Y in a regression problem, does the correlation change? a. Yes b. No
b. No
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? a. Yes b. No
b. No
Suppose we are doing a hypothesis test and α is set at 0.05. If our p-value turns out to be 0.07, we cannot reject Ho. However, would it be OK after the fact to change the significance level to something like 0.10, to make it so we could reject Ho? a. Yes b. No c. It depends on the situation
b. No
The density function for any continuous random variable X must be between 0 and 1 a. Yes b. No
b. No
Suppose you are using height (inches) to predict weight (pounds) in a regression situation. What are the units of the Y-intercept? a. Inches b. Pounds c. Pounds per inch d. No units
b. Pounds
If you were trying to predict someone's age using their years of employment, which variable would be the X variable? a. Age b. Years of employment c. Either variable is OK as the X variable, the results would be the same d. Not enough information to tell
b. Years of employment
If you increase n, what happens to the margin of error of your confidence interval for p? a. It increases b. It decreases c. It stays the same d. Not enough information to tell
b. it decreases
When you integrate e-x what do you get? a. e-x b. ex c. - e-x
c. - e-x
90% of students own an iPad. You take a random sample of 2 students. What's the probability that exactly one of them owns an iPad? a. .90 b. .09 c. .18 d. None of the above
c. .18
Suppose the probability density function f(x) for a uniform random variable X on the interval [0, 10]. What is the probability that X equals 5? a. 1/2 b. 1/10 c. 0 d. None of the above
c. 0
If X is a continuous random variable with f(x) = ½ for 0<x<2, what is the probability that X = 1? a. 1 b. ½ c. 0 d. None of the above
c. 0 (always 0 for a continuous random variable)
The owner of a restaurant claims that the time a customer takes to decide what they wanton the menu (X) has a mean of 3.2 minutes. (Assume X has a normal distribution with standard deviation .8 minutes.) You believe the mean is more than 3.2 minutes. Your sample of 25 customers chosen at random has a mean time of 3.6 minutes. What is your p-value? a. 2.5 b. 0.9938 c. 0.0062 d. 0.05
c. 0.0062 ((3.6-3.2)/(0.8/sqrt of 25))
Suppose you want to estimate the percentage of all OSU students who will take classes thissummer. 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? c. All OSU students d. The 100 OSU students who were sampled e. 30% f. The percentage of all OSU students who will take classes this summer
c. All OSU students
The formula for a confidence interval for p involves a Z-value. Why is this? (Assume n islarge.) 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
Bob's Z-score on an exam is 0.25. What is the correct interpretation? Circle one: a. Bob's score is 25 percentage points above the mean. b. Bob's score is at the 25th percentile. c. Bob's score is 0.25 standard deviations above the mean. d. Bob got a 25 on the exam
c. Bob's score is 0.25 standard deviations above the mean.
Bob wants to find the probability that X is at least 3. What probability does Bob need to find? a. P(X > 3) b. P(X < 3) c. P(X ≥ 3) d. P(X ≤ 3)
c. P(X ≥ 3)
What shape does the normal probability plot have if the data have a normal distribution? a. Scattered randomly about the line Y = 0 b. Bell-shaped curve c. Straight line going uphill d. None of the above
c. Straight line going uphill
In a hypothesis test, which of the following represents the significance level of the test? a. The p-value b. The confidence level c. The value of α d. The value of Z
c. The value of α
You are estimating the population mean and the standard deviation of the population is NOT known. Which distribution do you use in the confidence interval formula? a. Use a Z distribution. b. Use a t distribution with 30 degrees of freedom. c. Use a t distribution with n-1 degrees of freedom. d. Use a t distribution with n degrees of freedom
c. Use a t distribution with n-1 degrees of freedom.
Which of the following is a test statistic? a. p-value = .02 b. x bar=15.10 (this is a sample statistic, you have to change to Z to make it a test statistic) c. Z=-2.67 d. More than one of these answers is correct
c. Z=-2.67
If X is uniform on 5 to 10, what is its density function? a. f(x) = 1/10 b. f(x) = 5 c. f(x) = 1/5 d. Not enough information to tell
c. f(x) = 1/5
Suppose you take a random sample of size n and look at the average X bar. As n increases, which of the following statements is true about the mean of X bar? a. it increases b. it decreases c. it stays the same
c. it stays the same
You want to estimate the proportion of all students who will go home for winter break usinga confidence interval. Which condition(s) do you need to check in order to do this problem? a. n > 30 b. np≥10 and n(1-p) ≥10 c. np^ ≥ 10 and n(1-p^) ≥10 d. npo ≥ 10 and n(1-po) ≥10
c. np^ ≥ 10 and n(1-p^) ≥10
Suppose X has a normal distribution with mean 15 and standard deviation 5. What's the cutoff for the 10% highest values? a. .8997 b. 1.28 c. 8.6 d. 21.4
d. 21.4
Bob's Z-score on an exam is 0.25. What is the correct interpretation? Circle one: b. Bob's score is 25 percentage points above the mean. c. Bob scored better than 25% of the other students. d. Bob's score is 0.25 standard deviations above the mean.
d. Bob's score is 0.25 standard deviations above the mean
Which of the following situations involves the use of the Central Limit Theorem? a. X has a normal distribution and n is any value b. X has a normal distribution and n is > 30 c. X does not have a normal distribution (or is unknown) and n is any value d. X does not have a normal distribution (or is unknown) and n > 30
d. X does not have a normal distribution (or is unknown) and n > 30
The normal distribution is used to approximate a binomial distribution only if: a. The sample size n is greater than 30 b. The population proportion p is close to 0.50 c. The underlying population is normal d. np and n(1 - p) are both greater than or equal to 10
d. np and n(1-p) are both greater than or equal to 10
The 40th percentile of the standard normal (Z) distribution occurs at the number Z = 0.40 a. True b. False
B. False
P(Z < -2.74) = P(Z > 2.74) a. Yes b. No
a. Yes
If you get a new sample, which of the following elements of a hypothesis test will change? a. Your p-value b. Your significance level (this stays the same once it is set ahead of time.) c. Both a and b
a. Your p-value
The probability density function f(x) for a uniform random variable X for the interval [2, 10] is a. 𝑓(𝑥) = 1/8 b. 𝑓(𝑥) = 8 c. 𝑓(𝑥) = 1/10 d. None of the above
a. f(x) = 1/8
The Central Limit Theorem is an important result that pertains only to the _______ of the distribution of the random variable x bar a. shape b. mean c. standard error
a. shape
Variance of X formula
(x-mean)^2 times p(x)
If you sample 2500 people to estimate the proportion who own their own business, what is the approximate margin of error? Use the quick and dirty method
1/sqrt of 2500= .02
x bar = ux
FALSE
If X has a normal distribution with a mean of 60 and a standard deviation 6, what is the value of X if Z = 1.96? a. 71.76 b. 67.96 c. 61.96 d. None of the above
a. 71.76
The pizza place down Bob's street says they deliver their pizzas in 30 minutes or less.Bob thinks it takes longer. Bob conducts a hypothesis test. Suppose he makes a Type I error. What is the impact of this error? a. He would be wrongly accusing the pizza place of taking too long to deliver pizzas. b. The pizza place would keep delivering their pizzas in longer than 30 minutes but no one would catch it. c. None of the above.
a. He would be wrongly accusing the pizza place of taking too long to deliver pizzas.
Suppose someone reports that 70% of registered voters voted in the presidential election, and you think it's more than that. What technique to you use? a. Hypothesis test for a proportion. b. Confidence interval for a proportion. c. None of the above
a. Hypothesis test
Suppose it is assumed that the weight of yogurt containers have a normal distribution with mean 8 ounces and standard deviation 1 ounce. You believe the average weight is not 8 ounces. What technique do you use? a. Hypothesis test for mean, using Z b. Hypothesis test for proportion, using Z c. Hypothesis test for mean using t d. Confidence interval of some type
a. Hypothesis test for mean, using Z
In what situation do you reject Ho in a hypothesis test? a. If the p-value is less than α b. If the p-value is greater than α
a. If the p value is less than a
A 95% confidence interval for a population proportion is determined to be .75 to .86. As p-hat approaches ½ from either direction (above or below), what happens to the margin of error? a. increases b. stays the same c. decreases d. can't tell with the given information
a. Increases
As the population standard deviation increases, the margin of error: a. Increases b. Decreases c. Does not change
a. Increases
Suppose a random variable X is continuous with a certain density function f(x) where x > 0.You want to find P(X ≤ 5). What do you do? a. Integrate f(x) from 0 to 5. b. Take f(x) and plug in 5 for x c. Add up P(X =0) + P(X =1) + ... P(X = 5). d. None of the above
a. Integrate f(x) from 0 to 5.
The best fitting regression line is the one that has the _______________ sum of squares for error. a. Lowest b. Highest
a. Lowest
Is p value the sample proportion or the population proportion? a. Sample proportion b. Population proportion
a. Sample proportion
A confidence interval for the mean gives you a range of values that contains the exact population mean. a. Sometimes true b. Always true c. Never true
a. Sometimes true
What shape should a normal probability plot look like if you have a normal distribution? a. Straight line b. Bell-shaped curve. c. None of the above
a. Straight line
The Central Limit Theorem is important in statistics because it says: a. The distribution of is approximately normal, no matter what the distribution of X is, as long as n is large enough. b. The distribution of is approximately normal, no matter what the distribution of Xis, and no matter what the sample size is. c. The distribution of is normal if the distribution of X is normal
a. The distribution of is approximately normal, no matter what the distribution of X is, as long as n is large enough.
Let f(x) =1/3 be a density function for a random variable X where X is between 0 and 3.Which of the following represents the probability that X is 2? a. The integral of f(x) from 2 to 2 b. f(2) = 1/3 c. P(2) = 1/3 d. None of the above
a. The integral of f(x) from 2 to 2
Correlation measures the strength and direction of linear relationships only. a. True b. False
a. True
If Ha is not equal, the probability of being beyond the test statistic (the tail probability) is doubled for the p-value. a. True b. False
a. True
If you reject Ho in a hypothesis test for the mean, the value of Uo is guaranteed not to be the corresponding confidence interval. (Assume Ha is, alpha = .05, confidence level= 95%). a. True b. False
a. True
The coefficient of determination measures the % of variability in Y that is explained by X. a. True b. False
a. True
The p-values can change from sample to sample. a. True b. False
a. True
The variance of X+Y equals the variance of X plus the variance of Y if X and Y are independent. a. True b. False
a. True
You can have a line that does not go through any of the data points but has the best SSE. a. True b. False
a. True
Suppose you conducted a hypothesis test and you rejected Ho. Which type of error could you have made? a. Type I error only b. Type II error only c. You could have made both errors (Type I and Type II). d. Not enough information to tell
a. Type I error only
If you switch X and Y in a regression situation, does the slope of the regression line change? a. Yes b. No
a. Yes
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 = .25 and Ha: p > .25 b. Ho: p = .25 and Ha: p < .25 c. Ho: p > .25 and Ha: p = .25 d. Ho: p^ = .25 and Ha: p^ > .25
d. p^ = .25 and p^ > .25
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? g. The percentage of all OSU students who will take classes this summer h. 50 i. 200 j. 25%
j. 25%
Suppose 1063 people out of a random sample of 2054 adults report that they play video games.What is the standard error of p value? k. .0110 l. .0001 m. .4997 n. .2496
k. .0110 (square root of p(1-p)/p)
Suppose you want to estimate the percentage of all American families planning a vacation for thesummer. Your confidence interval is 30% to 40%. What was your value of ? r. 30% s. 40% t. 10% u. Unknown or none of the above
u. Unknown or none of the above