stats final quizzes

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 population in this problem?

all OSU students

a p-value for a test statistic in a hypothesis test represents the same value as the sample proportion.

false

a percentile is a percent

false

if X and Y are independent, then Variance of X-Y = Variance of X - Variance of Y.

false

if X has a uniform distribution with f(x) = 1/10 we know the values of X MUST go from 0 to 10; they can be nowhere else.

false

if X is binomial with n = 5 and p = 0.05, the chance that X is at least 1 is 0.6240.

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

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

what conditions do you need to check to find a probability for x-bar when x has a normal distribution?

no conditions to check -- only check when NO normal distribution

conditions for normal approximation to binomial

np and n(1-p) >= 10

what conditions do you need to check to do a 95% confidence interval?

np-hat and n(1-p-hat) at least 10

p(x > 10) or p(x-bar > 10) with n = 40, which probability is smaller?

p(x-bar > 10)

a data set with only 2 points will still have an SSE of 0 when you make its regression line

true

if X is a random variable with standard deviation 15, then the standard deviation of 2X is 30.

true

if X is continuous P(X < 4) = P(X <= 4)

true

if everything else stays the same, a 90% confidence interval is narrower than a 95% confidence interval

true

if independent, SD of (X - Y) = SD of (Y - X)

true

mu x bar = mu x

true

suppose X has a distribution with mean 10 and variance 4, Y has a distribution with mean 20 and variance 9. you can find the mean of X + Y with this information.

true

the margin of error of a confidence interval increases if the population has a higher standard deviation

true

the number of injuries sustained by an entire football team during a typical college football game is a discrete random variable.

true

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

true

which of the following is a condition of the binomial distribution?

- set number of trials - two outcomes (yes/no) - independent trials - fixed probability p

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

suppose X has a normal distribution with mean 10 and standard deviation 2. in order for the z-score to be equal to 0, then X must be equal to

10

when you are asked to provide a range of likely values for the average gas price in Columbus Ohio, what technique do you use?

Confidence Interval for the population mean

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

Mu with subscript X-bar

what is the symbol for the significance level of H Testing?

alpha

the formula for a confidence interval for p involves a z-value. why is this? (assume n is large enough)

because of the Central Limit Theorem

the normal distribution is an example of a _____________ distribution

continuous

what happens to the standard error of x bar as n approaches infinity?

decreases

suppose your confidence interval for the percentage of all American families planning a vacation for the summer is 30% to 40%. now suppose the media reported that 50% of American families go on vacation during the summer. based on your data, would you agree or disagree with them?

disagree

a binomial variable is what type of random variable?

discrete random variable

if X is a continuous random variable, which of the following conditions does NOT need to be checked to verify that f(x) is a legitimate probability distribution function?

f(x) must be less than or equal to 1

a p-value must be > alpha to reject Ho

false

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

false

suppose X has a distribution with mean 10 and variance 4, Y has a distribution with mean 20 and variance 9. we do not know whether X and Y are independent. however, we CAN still find the variance of X+Y with only the information given.

false

the value of alpha will change if you get a new data set

false

you can always interpret the y-intercept of the best fitting regression line

false

a residual is found by taking predicted value of Y minus the observed value of Y

false. residual = observed - predicted

which of the following variables is binomially distributed?

flipping a coin 10 times

what is the name of Dr. Rumsey's goat?

half-pint

suppose you found a 95% confidence interval for the mean using a random sample of size n, and you found it was too wide; that is, the margin of error was too large. if you wanted the margin of error to be 1/4 of what it was before, what do you have to do to the sample size?

increase it by 16 times what it was before

which of the following would increase the margin of error?

increase the confidence

if you increase n, what happens to the margin of error of your confidence interval for p?

it decreases

what is the name of my lead TA?

joel bracken

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

mu 0

is p-hat the sample proportion or the population proportion?

sample proportion

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

a company has developed a new battery, but the average lifetime of all 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

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

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

we should always add and subtract a margin of error because sample results vary

true

suppose you want to estimate the percentage of all American families planning a vacation for the summer. your confidence interval is 30% to 40%. what is your value of p-hat?

unknown or none of the above

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

we use statistics to estimate or test parameters

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

if your 95% confidence interval for the average gas price in Columbus Ohio turned out to be ($2.25, $2.75), do you know what the sample mean is?

yes

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 id n > 30

for a normal distributed variable X with mean 40 and standard deviation 10, what is the probability that X equals exactly 30? in notation, what is P(X = 30)?

0

if X has a continuous uniform distribution on the interval (50, 100), then what is P(x=75)?

0