Stats Final practice Multiple Choice Questions

The Z distribution is a special normal distribution whose mean is ____ and standard deviation is ____.

0, 1

17. Which of the following statements is always true? (If all are always true, select d) a. μx+y = μx + μy b. μxy = μx * μy c. 𝜎x + y 2 = 𝜎x 2 + 𝜎y 2 d. All of the above are always true.

A

Which of the following is a NOT a discrete random variable? a) The time between accidents on a busy highway. b) The number of accidents on a busy highway. c) The number of red cars that go by, in a random sample of 100. d) All of the above are discrete random variables.

A

23. Suppose the variance of X equals 3 and the variance of Y equals 2. Suppose also that X and Y are independent. Then the variance of X - Y equals 3 + 2 = 5. a. True b. False

A.

A two-tailed hypothesis test (meaning Ha is μ ≠ μo) is related to a confidence interval. If the value in H0 is not in the confidence interval, it means you ____________ H0. a. Reject b. Fail to reject

A.

After you find the Z-score, you find the probability of being at or beyond it, in the direction of your alternative hypothesis. What is this probability called? a. p-value b. H0 probability c. Significance level d. None of the above

A.

As the confidence level of your confidence interval increases, what happens to the value of Z*? a. Increases b. Decreases c. Stays the same

A.

As the standard deviation of the population increases, what happens to the MOE? a. Increases b. Decreases c. Stays the same

A.

For a two-tailed hypothesis test (meaning Ha is μ ≠μo) the further away your test statistic gets from 0 the more likely it is that you will reject Ho. a. True b. False

A.

If X has a normal distribution, could you find a probability for X bar if n was only 10? a. Yes, because X has a normal distribution already. b. No, because you always need n to be at least 30.

A.

If X has a normal distribution, then X bar has a normal distribution no matter what. a. True b. False

A.

If the values in the population are skewed, the sampling distribution of X bar can be approximated by the normal distribution if the sample contains at least 30 observations. a. True b. False

A.

If you have enough evidence against H0 and you are able to reject it, your p-value must have been: a. Small b. Large

A.

The shape of the normal distribution is: a. Symmetric b. Skewed c. Flat d. Unknown

A.

What aspects of X bar does the CLT apply to? a. Shape b. Mean c. Standard Error d. All of the above e. None of the above

A.

When X is a continuous random variable, P(X < 4) = P( X ≤ 4) a. True b. False

A.

Which of the following could possibly be a negative number? a. the set of possible values for X b. f(x) c. p(x) d. None of the above.

A.

Which of the following has a Binomial distribution? a. The number of people against a smoking ban out of a random sample of 100. b. The number of telephone calls received by a switchboard in a specified time period c. The number of customers arriving at a gas station on July 4 d. All of the above have a binomial distribution.

A.

19. If Corr (X, Y) = 0 (i.e. = 0), then X and Y are independent. a.True b. False

B

If X and Y are random variables with μX = 5 and μY = 8, then what is μ2X-3Y? a) -34 b) -14 c) 14 d) 34

B

Steven wonders what the average age is for all golfers that use his golf course. He randomly samples 50 golfers from his course and asks them to fill out a survey and include their age. He finds the average age is 43.5 years. Which statistical technique should Steven use now, to answer his original question? a. A hypothesis test b. A confidence interval c. Steven's done; he concludes that the answer to his original question is 43.5 years.

B

As n increases, what happens to the margin of error (MOE) of your confidence interval? a. Increases b. Decreases c. Stays the same

B.

As n increases, which of the following statements is true? a. The population standard deviation decreases. b. The standard error of the sample mean decreases. c. The population standard deviation increases. d. The standard error of the sample mean increases.

B.

For a two-tailed hypothesis test (meaning Ha is μ≠μo) the further away your test statistic gets from 0 the larger your p-value gets. a. True b. False

B.

If X is continuous, then f(2) stands for the probability that X = 2. a. True b. False

B.

If you are doing a hypothesis test for a population mean, you collect your data, find your statistic, and change it to a standard score (Z-score). What is the special name we give to this Z-score? a. p-value b. Test statistic c. Significance level d. None of the above

B.

If you are not able to reject H0, then you know H0 must be correct. a. True b. False

B.

Let X be the temperature of an oven in degrees Fahrenheit. The variance of X is also expressed in degrees Fahrenheit but the standard deviation is not. a. True b. False

B.

The 40th percentile of the standard normal (Z) distribution occurs at the number Z = 0.40 a. True b. False

B.

The closer your test statistic is to the middle of the Z-distribution, the ______ likely you are to reject H0. a. More b. Less

B.

The normal distribution is: a. Discrete b. Continuous

B.

The object of a hypothesis test is to challenge a claimed or reported value of a ___________________ using your data. a. sample statistic b. population parameter c. sample parameter d. population statistic

B.

The p-value is preset before the hypothesis test is conducted, but the significance level is unknown until the data has been collected. a. True b. False

B.

Which of the following can be a possible set of values for X when X is a continuous RV? a. X = 0, 1, 2, 3, ... b. X greater than or equal to 0 c. Both a and b are correct

B.

Which of the following is not a characteristic of a binomial distribution? a. There is a set of n trials b. Each trial results in more than one possible outcome. c. The trials are independent of each other. d. Probability of success p is the same from one trial to another.

B.

𝜎x - y 2 = 𝜎x 2 - 𝜎y 2 if X and Y are independent a. True b. False

B.

If X and Y are random variables with μx = 2 and μy = 8, then what is μ2X+3Y? a) 34 b) 13 c) 28 d) 40

C

Which of the follow statements is true? a) μax+b = μbx+a b) μax= μx + a c) μx+b = μx + b

C

10. Let X bar be the sample mean from X's distribution. The standard error of X bar is a. The same as the standard deviation of X b. Greater than the standard deviation of X c. Less than the standard deviation of X

C.

If X is a random variable with a standard deviation of 10, then 3X has a standard deviation equal to: a. 10 b. 3 c. 30 d. 90

C.

In the notation below, X is the random variable, c is a constant, and refers to the variance. Which of the following laws of variance is not correct? a. 𝜎x 2=0 b. σ2X+c=σ2X c. σ2X+c = σ2X + c d. σ2Xc = c^2σ2X

C.

Suppose X has a normal distribution and X bar represents the average of a sample of size n. Which of the following is true? a. has an approximate normal distribution for any value of n. b. has an approximate normal distribution if n is large enough. c. has an exact normal distribution for any value of n d. has an exact normal distribution if the sample size is large enough.

C.

Suppose X is always -3. Then 𝜎x 2 = a. -3 b. 9 c. 0 d. None of the above.

C.

The mean of a binomial probability distribution with n trials and probability p of success is: a. n + p b. np(1-p) c. np d. n + p - 1

C.

The population mean: a. Is always larger than or equal to the sample mean b. Is always smaller than or equal to the sample mean c. Can be smaller than, or larger than, or equal to the sample mean d. None of the above

C.

The mean of X bar equals the mean of X when a. Only if X has a normal distribution b. Only if n is large c. Both a and b are needed d. This statement is always true no matter what.

D

Consider the formula for the margin of error (MOE). Which components can the researcher control before the data is collected and analyzed? a. Sample size, n b. The population standard deviation c. The value of z* d. Bath a and c

D.

Suppose the mean of the random variable X equals 4 and the variance of X equals 3. Then the variance of 2X is equal to: a. 9 b. 2 c. 7 d. 12

D.

What proportion of the data from a normal distribution is within two standard deviations on either side of the mean? a. 0.3413 b. 0.4772 c. 0.6826 d. 0.9544

D.

Which of the following is not true for a standard normal (Z) distribution? a. It is symmetric. b. It has a mean of 0. c. It has a median of 0. d. The Z distribution is a discrete distribution

D.

Suppose X has a distribution with mean 10 and Y has a distribution with mean 20. The mean of X - Y is 30. a) True b) False

False

The number of accidents that occur at a certain intersection in a given year is a continuous random variable. a) True b) False

False

A z-value tellsyou how many _____ the X value is above (or below) its ____.

STANDARD DEVIATIONS, MEAN

If X is _______ the mean, the Z score will be a positive number. (above or below?)

above

The Z-table always gives you the probability of being _____ than the number you are looking up.

less

The Z distribution has a table that displays what type of probabilities: less-than or greater-than?

less than

If X is below the mean, the Z score will be a _______ number (positive or negative?)

negative

We use statistics to estimate population parameters, not the other way around.

true