Stats Test 2

With all other things kept constant, an increased sample size will decrease the width of a confidence interval.

sample size

Which formula gives the standard deviation for a binomial distribution? A. σ = np B. σ= √npq C. s= σn D. s=xpn

σ= √npq

The more confident you are that an interval contains the population mean, ________________. A.the larger the interval is B. the larger the α C.the smaller the sample size D.the larger the error bound

the larger the interval is

Which of the following random variables is discrete? A. the time spent waiting for a bus at the bus stop B. the mass of a test cylinder of concrete C. the amount of water traveling over a waterfall in one minute D. the number of heads tossed on four distinct coins

the number of heads tossed on four distinct coins

Which of the following is NOT a characteristic of a binomial distribution? A. there are fixed number of trials B. there are only two possible outcomes, successes and failures C. the trials are independent and repeated using D. the probability of success converges to 0.50

the probability of success converges to 0.50

A government agency was charged by the legislature with estimating the length of time it takes citizens to fill out various forms. The agency generated an 85% confidence interval, a 90% confidence interval, and a 99% confidence interval, all of which are listed below. Which one is the 90% confidence interval? A(12.63, 12.97) B.(12.49, 13.11) C.(12.60, 13.00)

(12.60,13.00)

A government agency was charged by the legislature with estimating the length of time it takes citizens to fill out various forms. The agency generated an 85% confidence interval, a 90% confidence interval, and a 99% confidence interval, all of which are listed below. Which one is the 85% confidence interval? A. (12.60, 13.00) B. (12.49, 13.11) C. (12.63, 12.97)

(12.63, 12.97)

What is the range of probabilities for an event A? A. 0<P(A) B. 0<P(A)<1 C. -1<P(A)<1 D.-Infinity<P(A)<Infinity

0<P(A)<1

The probability distribution of a discrete random variable x is shown in the following table. The standard deviation σ of the random variable x is about: A. 3.12 B. 1.96 C. 2.27 D. 0.59 E. 1.27

1.27

You roll a fair six-sided die. Find the probability of event B: rolling a 4. A. 3/6 B. 1/6 C. 4/6 D. 2/6 E. 0

1/6

The standard normal distribution has a mean of ____ and a standard deviation of ______. A. 0,1 B. 1,0

0,1

The following two-way contingency table gives the breakdown of the population in a particular locale according to party affiliation (A, B, C, or None) and opinion on a bond issue. A person is selected at random. The probability that the person has no party affiliation AND is undecided is

0.03

The following two-way contingency table gives the breakdown of the population of adults in a particular locale according to highest level of education and whether or not the individual regularly takes dietary supplements. An adult is selected at random. The probability that the person's highest level of education is a high school diploma and that the person takes dietary supplements regularly is

0.06

For a 90% confidence interval, α= [ Select ] ["0.025", "0.90", "0.10", "0.05", "0.20"] , and α/2= [ Select ] ["0.15", "0.025", "0.10", "0.20", "0.05"] .

0.10, 0.05

Imagine an experiment where a coin is flipped 3 times. Assuming that the coin is fair, what is the probability of the coin landing heads more often than tails? (A)0 (B)1 (C).66667 (D).50 (E)0.25

0.50

The training heart rates of all athletes are normally distributed, with mean 135 bpm and standard deviation 18 bpm. Random samples of 4 are drawn, and the mean of each is found. Find the mean of the sampling distribution. A. 135/18 B. 135/√4 C. √135/4 D. 135

135

A sample of 20 bee hives is taken to monitor their health. The beekeeper finds the sample average hive weight is 75 lb with a standard deviation of 3 lb. What are the degrees of freedom? Group of answer choices A. 19 B. (72,78) C. 3 D. 3/20

19

You roll a fair six-sided die. Find the probability of event C: rolling a number less than 5. A. P(C) = 2/6 B. P(C) = 3/6 C. P(C) = 5/6 D. P(C) = 4/6 E. P(C) = 1/6

4/6

A survey shows that people use cell phones an average of 1.5 years with a standard deviation of 0.5 years. A user is randomly selected. If cell phone use is normally distributed, we can use Excel to calculate the probability that the randomly selected user uses their phone for more than 1 year with the function: A. =1- NORM.INV(1, 1.5, 0.5) B. =NORM.INV(1, 1.5, 0.5) C. =NORM.DIST(1, 1.5, 0.5, FALSE) D. =1 - NORM.DIST(1, 1.5, 0.5, TRUE) E. =NORM.DIST(1, 1.5, 0.5, TRUE)

=1 - NORM.DIST(1, 1.5, 0.5, TRUE)

Admissions wants to estimate the mean age of students. In a random sample of 20 students, the mean is 22.9 years and the standard deviation is 1.5. Assuming that student age is normally distributed, you decide to construct a 90% CI of the mean student age. Which Excel function will you use to calculate the EBM? A.=CONFIDENCE.T() B. =T.CONF() C. =CONFIDENCE.NORM() D. =NORM.CONF()

=CONFIDENCE.T()

Find the cumulative area that corresponds to a z-score of 0.24 A. =NORM.DIST(0.24, 0, 1, TRUE) B. Not enough information is given C. =NORM.DIST(0.76, 0, 1, TRUE) D. =NORM.INV(0.24, 0, 1)

=NORM.DIST(0.24, 0, 1, TRUE)

A statistician wants to find the probability that a z score is between 1 and 2.5. Which of these functions gives the probability? Group of answer choices A. Not enough information - the mean and standard deviation and not given B. =NORM.DIST(2.5-1,0,1,TRUE) C. =NORM.DIST(2.5,-1,0,1,FALSE) D. =NORM.DIST(2.5,0,1,TRUE)-NORM.DIST(1,0,1,TRUE) E. =NORM.DIST(2.5,0,1,TRUE)+NORM.DIST(1,0,1, TRUE) F. Not enough information - the n is not given

=NORM.DIST(2.5,0,1,TRUE)-NORM.DIST(1,0,1,TRUE)

An ornithologist wants to know the probability that a randomly selected male kakapo (owl parrot) is between 3 and 7 lb. A sample of 39 males showed their mean weight is 4.5 lb with a standard deviation of 2 lb. What function gives this probability? A. =T.DIST(7,4.5,2,TRUE)-T.DIST(3,4.5,2,TRUE) B. =NORM.DIST(7,4.5,2/SQRT(39),TRUE)+NORM.DIST(3,4.5,2/QRT(39),TRUE) C. =NORM.DIST(7,4.5,2/SQRT(39),TRUE)-NORM.DIST(3,4.5,2/SQRT(39),TRUE) D.=NORM.DIST(7-3,4.5,2,TRUE) E. =NORM.DIST(7,4.5,2,TRUE)-NORM.DIST(3,4.5,2,TRUE)

=NORM.DIST(7,4.5,2,TRUE)-NORM.DIST(3,4.5,2,TRUE)

A randomly selected sample of size 19 has a mean of 3 and a standard deviation of 1. Assume the population is normally distributed. Which function finds the probability that t is less than 1.3? A. =T.DIST(1.3, 18, TRUE) B. = T.DIST(1.3, 19, FALSE) C. =T.DIST(1.3, 3, 1/SQRT(19), TRUE) D. T.DIST(1.3- 1, 3, 1, TRUE) E. = 1 - T.DIST(1.3, 18, TRUE) F. =T.DIST(1.3 0, 1, TRUE) G. =T.DIST(1.3, 3, 1, TRUE) H. =T.DIST(1 - 1.3, 18, TRUE) I. =T.DIST(1.3, 19, TRUE) J. =1 - T.DIST(1.3, 19, TRUE) K. =T.DIST(1.3 - 1, 19, TRUE) L. =1 - T.DIST(1.3, 3, 1, TRUE) M =Z.DIST(1.3 3, 1, TRUE)-

=T.DIST(1.3,18,TRUE)

A voter wants to know how much time governors spend on golf courses per year. He finds data on 12 governors. The sample average is 48 days with standard deviation 10 days. Assume the population amount of time is not normally distributed. Which of the following the critical value if he wants to build a range that is 90% likely to contain the true population average? A. =T.INV((1-0.90)/2, 48, 10/SQRT(12)) B.=T.INV((1-0.90)/2, 0, 1) C. =T.INV((1-0.90)/2, 12)=NORM.INV((1-0.90)/2, 0, 1)= D. T.INV((1-0.90)/2, 11)

=T.INV((1-0.90)/2,11)

The probability a person who reserved a trip on a 12-vehicle ferry will not arrive is 0.15. The ferry company makes 13 reservations for a particular trip, and we want to find the chance that all 13 vehicles show. What is a "success"? A. All 12 reservations not showing up B. A person who reserved a trip not showing up C. A person who reserved a trip showing up D. All 13 reservations not showing up E. All 12 reservations showing up F. All 13 reservations showing up

A person who reserved a trip showing up

The mean monthly salary of a random sample of 20 college graduates under the age of 30 was found to be $1320 with a standard deviation of $677. Assume that the distribution of salaries for all college graduates under the age of 30 is normally distributed. Suppose a 90% confidence interval for the population mean of monthly salaries of all college graduates under the age of 30 was calculated. Which of the following would produce a narrower interval than the 90% confidence interval? A. A 95% confidence interval rather than a 90% confidence interval. B. A sample with a standard deviation of 1000 instead of 677. C. A sample of size 28 instead of 20. D. A sample of size 15 instead of 20. E. A sample with a standard deviation of 725 instead of 677.

A sample of size 28 instead of 20.

The standard normal distribution has more probability in its tails than the t distribution. A. True B. False

False

A chef wants to make a dish that scales with the size of the potato used. If the potato is above 2.5 in in diameter or below 1.5 in diameter, he must change the other ingredients. He takes a sample of 40 random potatoes and finds their mean diameter is 1.75 in with a standard deviation of 0.1 in. What is the probability that a randomly selected potato is above 2.5" or below 1.5"? A. =NORM.DIST(1.5,1.75,0.1,TRUE)+(1-NORM.DIST(2.5,1.75,0.1,TRUE)) B. =NORM.DIST(1.5,1.75,0.1,TRUE)-NORM.DIST(2.5,1.75,0.1,TRUE) C. =NORM.DIST(1.5,1.75,0.1,TRUE)+NORM.DIST(2.5,1.75,0.1,TRUE) D. =NORM.DIST(2.5,1.75,0.1,TRUE)-NORM.DIST(1.5,1.75,0.1,TRUE)

NORM.DIST(1.5,1.75,0.1,TRUE)+(1-NORM.DIST(2.5,1.75,0.1,TRUE))

To find the z-score corresponding to a right tail area of 0.25 in Excel we would use: A. =T.INV(0.25, 0, 1) B. =NORM.DIST(0.25, 0, 1, TRUE) C. =NORM.DIST(0.25, 0, 1, FALSE) D. =NORM.INV(1-0.25, 0, 1) E. =NORM.INV(0.25, 0, 1)

NORM.INV(1-0.25,0,1)

Which of the following is a possible probability for an event A? A. P(A) = 112% B. P(A) = 1.10 C. P(A) = 0 D. P(A) = -0.50

P(A)=0

To calculate the probability that an event A is between b and c, where b<c, you use the formula: A. P(b ≤ A ≤ c) = c-b/n where n is the total number of possible outcomes B. P(b ≤ A ≤ c) = P(A ≤ c) - P (A ≤ b) C. P (b ≤ A ≤ c) = P(c) - P(b) D. P(b ≤ A ≤ c) = P(b) + P(c) - P ( b u c)

P(b ≤ A ≤ c) = P(A ≤ c) - P (A ≤ b)

An economist samples 20 Fortune 500 companies and finds they have an average CEO salary of $11.5 million with a standard deviation of $2 million. She wants to know what t-value corresponds to a probability of 0.75. Which function finds this in Excel? A. =T.INV(0.75, 20) B. =T.DIST(0.75, 19, TRUE) C. =T.INV(0.75, 19) D. =T.DIST(0.75, 20, FALSE) E. =T.DIST(0.75, 20, TRUE) F. =T.DIST(0.75, 19, FALSE)

T.INV(0.75,19)

Which of the following are NOT properties of the normal distribution? A. centered at 0 with standard deviation of 1. B. total area under the curve is equal to 1. C. the mean, median, and mode are all equal. D. symmetric about the mean.

centered at 0 with standard deviation of 1.

For any distribution, the distribution of individual values, x, approaches a normal distribution as more samples are taken.

false

Which of the following is NOT a property of the t distribution? Group of answer choices A. As the sample size grows, it approximates the normal distribution B. The shape changes with the degrees of freedom C. It has less probability in its tails than the z distribution D. Symmetric about the mean

it has less probability in its tails than the z distribution

The more samples a researcher takes, the _______________ the confidence interval. A. less wide B. less normalized C. wider D. more uncertain

less wide

Is the following considered a probability distribution?

no because 0<P(x)<1

In a random sample of 19 patients at a hospital's emergency department, the mean waiting time before seeing a medical professional was 23 min and the standard deviation was 11 min. Assume the waiting times are not normally distributed. Which distribution would this situation call for? A. z-distribution B. normal distribution C. t-distribution D. more information is needed E. no distribution can be used without applying the CLT

t-distribution

Which formula gives the mean for a binomial distribution? A. u=np B. u=xn C. u=1/2x D. u=npq

u=np

Food scientists conduct a survey of randomly selected individuals to find out the percentage of people who think a hot dog is a sandwich. What distribution should they use to make a confidence interval for the population proportion? A. z distribution B. They should use either a z or t distribution depending on how big their sample size is. C. t distribution D. p distribution E. c distribution

z distribution

A random sample of 4,000 students was taken to see the average amount of time students spend on the computer per day. Computer science students heavily skewed the data. Which distribution would this situation call for? A. c distribution B. more information is needed C. z distribution D. t-distribution

z-distribution