STATS quizes

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 ¼ of what it was before, what do you have to do to the sample size? - increase it by 4 times what it was before - decrease it by 1/4 of what it was before -increase it by 16 times what it was before - none of the above

increase it by 16 times what it was before

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? - mu x - mu 0 -xbar

mu 0 Ho: Mux = Mu0

If X has a normal distribution, which of the following is true about the shape (distribution) of the random variable X-bar? - xbar is approximately normal for any n - xbar is exactly normal if n> 30 - xbar is approximately normal if n> 30 - xbar is exactly normal for any n

xbar is exactly normal for any n

Which of the following is NOT a condition of the binomial distribution? -set number of trials -two outcomes -independent trials -fixed probability p -none of the above

-none of the above

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 ~ 0 ~ 2 ~ none of the above ~ 10

10

If the Z-score is 1.96, and X has a normal distribution with mean 60 and standard deviation 6, what X-value corresponds to this Z-score? - 71.76 - 48.24 - 61.96 - 67.96

71.76

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 we are given. -true -false

false

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

false

What is the symbol we use to represent the mean of the random variable X-bar? -mu with subscript x -mu with subscript xbar -capital xbar

mu with subscript xbar

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 can be any value -np ≥ 10 - n> 30 -np at least 10 and n(1-p) at least 10

n> 30

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

sample proportion

If X has a continuous uniform distribution on the interval (0,5), what is the 25th percentile for X? - 0.25 - 1.25 -none of the above - 25%

1.25

If X has a continuous uniform distribution on the interval (50, 100), then what is P(X=75)? - 1/100 - 1/50 -none of the above - 1/75 - 0

1/50

If X has a continuous uniform distribution on the interval (50, 100), then what is f(75)? - 1/50 - none of the above - 1/100

1/50

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 -92.3 -74.8 -84.7

78.4

If X is binomial with n = 5 and p = 0.05, the chance that X is at least 1 is 0.6240 -true -false

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%. -true -false

false

Which of the following variables is binomially distributed? -flipping a coin until you get heads - flipping a coin 10 times - both of the above -neither of the above

flipping a coin 10 times

The formula for a confidence interval for p involves a Z-value. Why is this? (Assume n is large.) - because the original distribution was a normal distribution - becuase you always use Z in any confidence interval - because of the central limit theorem

because of the central limit theorem

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 -false

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 was your value of p-hat? -30% -40% -10% -unknown or none of the above

unknown or non of the above

Which of the following describes the relationship between parameters and statistics? -we use parameters to estimate or test statistic -we use statistics to estimate or test parameters - statistics and parameters are the same thing

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? - xbar is exactly normal for any n - xbar is approximately normal for any n - xbar is exactly normal if n> 30 - xbar is approximately normal if n> 30

xbar is approximately normal is n> 30

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 was? -yes -no

yes

The set of all possible sample means from all possible samples of size n from the population is known as the: -not enough information to tell -population probability distribution of x -sample mean of the population of x - sampling distribution of xbar

sampling distribution of xbar

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 -parameter -population -sample

statistic

Which of the following is true about the mean of the random variable X-bar as n increases? -the mean of xbar increases -the mean of xbar stays the sam e -not enough info to tell -the mean of xbar decreases

the mean of xbar stays the same

The margin of error of a confidence interval increases if the population has a higher standard deviation. -true -false

true

The number of injuries sustained by an entire football team during a typical college football game is a discrete random variable. -true -false

true

If everything else stays the same, a 90% confidence interval is narrower than a 95% confidence interval. -true -false

true - a 95% confidence interval contains more values

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 above the mean - 1.5 standard deviations below the mean - 0.066 standard deviations above the mean - 0.066 standard deviations below the mean

- 1.5 standard deviations below the mean

Where is the 10th percentile of the Z distribution? - .90 - 1.28 - -1.28 - 0.1

-1.28

A binomial random variable is what type of random variable? -continuous random variable -discrete random variable -both -neither

-discrete random variable

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

-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 no where else. -true -false

-true -false

For a normally distributed variable X with mean 40 and standard deviation 10, what is the probability that X equals exactly 30? In notation, what is P\left(X=30\right)P(X=30)P(X=30) ? - 0.159 - 0.242 - 0.841 - 0

0

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? - Ho: p = 0.25 vs. Ha: p > 0.25 - Ho: p = 0.25 vs. Ha: p \ne 0.25 - Ho: p > 0.25 vs. Ha: p = 0.25 - Ho: p-hat = 0.25 vs. Ha: p-hat \ne 0.25

Ho: p = 0.25 vs. Ha: p > 0.25

When you are asked to provide a range of likely values for the average gas price in Columbus Ohio, what technique do you use? -hypothesis test for the population mean -confidence interval for the population mean - hypothesis test for the sample mean -confidence interval for the sample mean

confidence interval for the population mean

The Normal distribution is an example of a _________________ Distribution. -neither -continuous -discrete

continuous

Which of the following would increase the Margin of Error? -decrease the standard deviation - increase the confidence - increase the sample size

increase the confidence

The Central Limit theorem tells us important results that pertain to: -the mean of the distribution of xbar -all of the above -the standard error of the distribution of xbar -the shape (type) of the distribution of xbar

the shape (type) of

Which of the following is true about the standard error of the random variable X-bar as n increases? -Not enough information to tell. -The standard error of X-bar decreases. -The standard error of X-bar increases. -The standard error of X-bar stays the same.

the standard error of xbar decreases

If X is a random variable with standard deviation 15, then the standard deviation of 2X is 30. -true -false

true

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

true

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? -the 200 OSU students who were sampled -the percentage of all OSU students who will take classes this summer - all OSU students - all OSU students who will take classes this summer

all OSU students

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? -agree -disagree -not enough info to tell

disagree

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 integrate to 1 -f(x) must be greater than or equal to 0 -f(x) must be less than or equal to 1 -all of the above must be checked

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

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

false

If X and Y are independent, then Variance of X-Y = Variance of X - Variance of Y -true -false

false

If you increase n, what happens to the margin of error of your confidence interval for p? -it increases -it decreases -it stays the same

it decreases