Stat 1430 Final Exam

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

False

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

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

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

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

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 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 you want to estimate the average age of all Pokemon players. Would you use a confidence interval or a hypothesis test?

A confidence interval

Which of the following is a condition of the binomial distribution? same probability of yes on each trial (p) fixed number of trials (n) independent trials two possible outcomes on each trial (yes/no)

All Answers

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

Correlation changes which X and Y are switched

False

Failing to reject Ho and Accepting Ho are both appropriate conclusions that mean the same thing.

False

If your test statistic is negative, so is your p-value.

False

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

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 standard deviation of X minus Y is solved by subtracting the standard deviation of X from the standard deviation of Y only if independent

False

The t distribution is taller and thinner (more concentrated around the mean) than the Z distribution.

False

When you integrate e^-x , you get e^-x

False

Which of the following variables has a binomial distribution? Flipping a coin 10 times and counting the number of heads. Flipping a coin until you get 10 heads and counting the number of flips needed.

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

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 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

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

True

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

below

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

True

Correlation is affected by outliers.

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

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

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

True

The mean of X minus Y is solved by subtracting the mean of X from the mean of Y in all cases even if not independent

True

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

True

The variance of X minus Y is solved by subtracting the variance of X from the variance of Y only if independent

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

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 ( Use x to predict Y)

If you reject Ho, which type of error could you be making?

Type 1 Error

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

Uncountably infinite

Bottles of cream have a normal distribution with a mean of 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 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

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

Mu with subscript X-bar

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?

Muo

Which of the following is NOT a continuous random variable? Time waiting on the phone for tech support (in seconds) Length of time between accidents at an intersection Number of accidents in one year at an intersection

Number of accidents in one year at an intersection

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

Random patterns, No fan shapes, Points fall around the horizontal line Y = 0

If you don't know the population standard deviation, what do you use as a substitute in your test statistic?

S

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 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

What does SSE stand for?

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

What 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

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

The standard error of X-bar decreases.

Which of the following describes the relationship between parameters and statistics? Statistics and parameters are the same thing We use statistics to estimate or test parameters We use parameters to estimate or test 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 approximately normal if n > 30 X-bar is approximately normal for any n X-bar is exactly normal if n > 30 X-bar is exactly normal for any n

X-bar is exactly normal for any n

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.