stats final: 2

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

a

An insurance company study shows that 60% of the auto insurance claims submitted for property damage were submitted by males under 25 years of age. Suppose 8 property damage claims involving automobiles are selected at random from that region. Let x be the number of claims (among the 8 selected) that were made by males under the age of 25. To find the probability that exactly 6 of the 8 claims are made by males under 25, we would use the binomial distribution with n=____

8

To calculate z α / 2 in Excel, use the function _____ .

=NORM.INV(1-alpha/2, 0, 1)

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) = 4/6 D. P(C) = 1/6 E. P(C) = ⅚

c

A synthetic fiber used in manufacturing carpet has tensile strength that is normally distributed with mean 75.0 psi and standard deviation 10.0 psi. For a sample of 100 fibers, we can calculate the probability that the sample mean is less than 71 psi using the excel command: A. =T.DIST() B. =NORM.DIST() C. =T.INV() D. =NORM.INV() E. =CONFIDENCE.T()

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)

C

If you are constructing a 95% confidence interval for a normally distributed population when your sample size is 10, what critical value should you use? A. z0.05 B. t0.025 C. t0.05 D. z0.025

C

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. t-distribution C. no distribution can be used without applying the CLT D. more information is needed E. normal distribution

E

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)

d

A z-score of 1 means that _____ A. very unusual. B. non-negative. C. a value is one variance away from the mean. D. a value is one standard deviation away from the mean.

d

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

sample size

For a 90% confidence interval, α= ____ , and α / 2= ____.

0.10,0.05

An insurance company study shows that 60% of the auto insurance claims submitted for property damage were submitted by males under 25 years of age. Suppose 8 property damage claims involving automobiles are selected at random from that region. Let x be the number of claims (among the 8 selected) that were made by males under the age of 25. To find the probability that exactly 6 of the 8 claims are made by males under 25, we would use the binomial distribution with p= ____.

0.6

Samples of rejuvenated mitochondria are mutated (defective) in 1% of cases. Suppose that 150 samples are studied. If X is the number of mutated mitochondria in the sample, then X is binomial with n= ____, p = ____.

150, 0.01

17% of victims of financial fraud know the perpetrator of the fraud personally. Let X be the number of people in a random sample of 25 victims of financial fraud who knew the perpetrator personally. Then X is binomial with n = ____, p = _____

25, 0.17

In a random experiment a fair die is rolled seven times. If the random variable Y counts the number of times a 3 is rolled, then X is a binomial random variable with two parameters n = ____, p = ____

7, 1/6

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

A

A city government asks 500 randomly selected people whether or not they are employed. The population percentage of employment is 0.60. Which equation would calculate the probability that less than 300 of these people are employed? A. =BINOM.DIST(300, 500, 0.60, TRUE) B. =NORM.DIST(300, 0.60, 500/SQRT(300),TRUE) C. =T.DIST(300, 499, TRUE) D. =BINOM.DIST(300, 500, 0.60, FALSE)

A

A randomly selected sample of size 19 has a mean of 3 and a standard deviation of 1. Assume the population is normally distributed. 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)-

A

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. p distribution C. They should use either a z or t distribution depending on how big their sample size is. D. t distribution E. c distribution

A

Suppose we are working within a normal distribution. Which function finds an event's value given the probability of an event? A. =NORM.DIST() B. =NORM.INV() C. =PROBABILITY() D. =STAND.DIST()

A

The sampling distribution of sample means _____________. A. can be used to create a confidence interval for the population mean. B. becomes more skewed with each additional sample. C. always approximates a normal distribution. D. has the same mean and standard deviation as any one sample.

A

Which equation corresponds to the expected value of an experiment with n samples, random variable x, probability P(x), confidence level c, and standard deviation s? A. ∑ x * P(x) B. ∑ x * s/c C. ∑ x/P(x) D. = (1-c)/2 * s/√n

A

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

A

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, 3, 1, TRUE) B. =T.DIST(1.3, 18, TRUE) C. =T.DIST(1- 1.3, 18, TRUE) D. =1 - T.DIST(1.3, 19, TRUE) E. =T.DIST(1.3 0, 1, TRUE) F. =T.DIST(1.3, 3, 1/SQRT(19), TRUE) G. = T.DIST(1.3, 19, FALSE) H. T.DIST(1.3 - 1, 3, 1, TRUE) I. =Z.DIST(1.3 3, 1, TRUE) J. =T.DIST(1.3, 19, TRUE) K. =1 - T.DIST(1.3, 3, 1, TRUE) L. = 1 - T.DIST(1.3, 18, TRUE) M. =T.DIST(1.3 - 1, 19, TRUE)

B

The law of large numbers states that ________________. A. as more trials are undertaken, the expected value approaches 0. B. as the number of trials increases, the experimental probability approaches the theoretical probability. C. the larger the mean, the greater the standard deviation for an experiment. D. the theoretical mean is larger than the experimental mean.

B

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

B

The standard normal distribution has a mean of ____ and a standard deviation of ______. A. x̄, s/√n B. 0,1 C. μ, σ^2 D. 1,0

b

Cell phone bills for a city's residents have a mean of $63 and a standard deviation of $11. Random samples of 100 bills are drawn from this population, and the mean of each sample is found. What is the mean of the sampling distribution? A. 11 B. 0.11 C. 0.63 D. 63 E. 6.3

D

If A = {3, 6, 9, 10} and B = {3, 4, 5, 6}, what is A ∪ B? A. {4, 5, 9, 10} B. {3, 6} C. {3, 6, 9} D. {3, 4, 5, 6, 9, 10}

D

In a survey of 100 U.S. adults, 66 said that it is acceptable to check personal e-mail while at work. What is the sample proportion of failures? A. 1.52 B. 0.44 C. 0.66 D. 0.34

D

Suppose we are working within a normal distribution. Which function finds an event's value given the probability of an event? A. =NORM.DIST() B. =PROBABILITY() C. =STAND.DIST() D. =NORM.INV()

D

The amount of multivitamin gummies eaten by college students in a 1-month period is normally distributed with a mean of 25 and standard deviation of 3. Find the confidence interval for the mean amount of gummies eaten in a month by a random sample of twelve college students if the given error bound is 5. A. (25-3/√12, 25+3/√12) B. (22,28) C. (20,30) D. (25-15/√12, 25+15/√12)

C

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

C

The probability that T takes on a value between -t0.05 and t0.05 is: A. 0.95 B. 0.80 C. 0.90 D. 0.05 E. 0.85

C

Suppose we are working within a normal distribution. Which function finds the cumulative probability of an event given that event's value? A. =STAND.NORM() B. =NORM.INV() C. =PROBABILITY() D. =NORM.DIST()

D

The probability that T takes on a value between -t0.10 and t0.10 is: A. 0.95 B. 0.05 C. 0.85 D. 0.80 E. 0.90

D

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.

E

A z-score of 1 means that A. non-negative. B. a value is one standard deviation away from the mean. C. very unusual. D. a value is one variance away from the mean

b

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

a

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 less than 1 year with the function: A. =NORM.DIST(1, 1.5, 0.5, TRUE) B. =1- NORM.INV(1, 1.5, 0.5) C. =NORM.INV(1, 1.5, 0.5) D. =1 - NORM.DIST(1, 1.5, 0.5, FALSE) E. =1 - NORM.DIST(1, 1.5, 0.5, TRUE)

a

Find the area to the right of a z-score of z = -0.85. A. =1- NORM.DIST(-0.85, 0, 1, TRUE) B. Impossible. Z scores must be positive. C. =NORM.DIST(1-(-0.85), 0, 1, TRUE) D. Not enough information given. E. =NORM.DIST(-0.85, 0, 1, TRUE)

a

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)

a

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

a

What happens to the mean and standard deviation of the distribution of sample means as the size of the sample increases? A. The mean of the sample means stays constant and the standard error decreases. B. The mean of the sample means decreases and the standard error increases. C. The mean of the sample means increases and the standard error stays constant. D. The mean of the sample means decreases and the standard error decreases. E. The mean of the sample means increases and the standard error decreases. F. The mean of the sample means stays constant and the standard error increases. G. The mean of the sample means increases and the standard error increases. H. The mean of the sample means decreases and the standard error stays constant. I. The mean of the sample means stays constant and the standard error stays constant.

a

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.

a

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

a

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. =NORM.DIST(7, 4.5, 2, TRUE) - NORM.DIST(3, 4.5, 2, TRUE) B. =NORM.DIST(7-3, 4.5, 2, TRUE) C. =NORM.DIST(7, 4.5, 2/SQRT(39), TRUE) + NORM.DIST(3, 4.5, 2/SQRT(39), TRUE) D. =NORM.DIST(7, 4.5, 2/SQRT(39), TRUE) - NORM.DIST(3, 4.5, 2/SQRT(39), TRUE) E. =T.DIST(7, 4.5, 2, TRUE) - T.DIST(3, 4.5, 2, TRUE)

answer needed

Which of the following functions finds the probability that t is between -1.2 and 0.5 for a sample size of 12? A. =T.DIST( 0.5- 1.2), 12, FALSE) B. =T.DIST(0.5, 12, FALSE) - T.DIST(-1.2, 12, FALSE) C. =T.DIST(-1.2, 12, TRUE) - T.DIST(0.5, 11, TRUE) D. =T.DIST(0.5, 11, TRUE) - T.DIST(-1.2, 11, TRUE) E. =T.DIST(0.5, 12, TRUE) - T.DIST(-1.2, 12, TRUE) F. =T.DIST( 0.5 - (1.2), 12, TRUE) G. =T.DIST( 0.5 - (1.2), 11, FALSE)

answer needed

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. (12.49, 13.11) B. (12.60, 13.00) C. (12.63, 12.97)

b

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)

b

When estimating a population parameter, a point estimate is A. the population mean. B. a statistic that estimates a population parameter. C. a range of possible values for the population parameter. D. always equal to the population value.

b

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

b

If, after you obtain a 95% confidence interval , you find it to be too narrow, which of the following steps can you take to increase the width (i.e. E gets larger) of the confidence interval? (choose all that apply) A. Construct a 99% confidence interval instead of a 95% one. B. Construct a 90% confidence interval instead of a 95% one. C. Re-do the 95% confidence interval using a smaller sample size. D. Re-do the 95% confidence interval using a larger sample size.

b, c

A sample space is _______________________. A. the results of a specific sample in an experiment. B. the amount of samples taken. C. the set of all possible outcomes in an experiment. D. the distribution of sample means.

c

Which of the following is NOT a property of the standard normal distribution? A. the total area under the curve is equal to 1. B. symmetric about the mean. C. uniform in shape. D. centered at 0 with standard deviation of 1. E. bell-shaped

c

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

c

A soda company wants to estimate the population proportion of people who drink soda with confidence level c, so they take a sample of 45 people. What equation gives their critical value? A. =NORM.DIST(c, 0, 1, TRUE) B. =NORM.DIST((1-c)/2, 0, 1, FALSE) C. =NORM.INV(c, 0, 1, TRUE) D. =NORM.INV((1-c)/2, 0, 1)

d

If a population is heavily skewed to the right, can we use the central limit theorem? A. No, the central limit theorem does not adjust for skew. Another method is needed. B. Yes, we can use the central limit theorem with any population. C. No, we must use the t-distribution. D. Yes, if enough samples are taken

d

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

d

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 standard error of the mean A. 18/4 B. 18 C. 18^2 D. 18/√4 E. √18

d

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)

d

Which formula gives the mean for a binomial distribution? A. μ=npq B. μ=½x C. μ=xn D. μ=np

d

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

d

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

d

You roll a fair 6 sided die. Find the probability of event B rolling a 4. A. 0 B. 3/6 C. 2/6 D. ⅙ E. 4/6

d

Suppose that 40% of all Charlotte voters favor a particular political candidate. You take a poll of 100 Charlotte voters. If the random variable X denotes the number of voters in your sample who favor the candidate, then the mean of X is: A. 24 B. 5 C. 38 D. 60 E. 40-

e

What happens to the mean and standard deviation of the distribution of sample means as the size of the sample decreases? A. The mean of the sample means stays constant and the standard error decreases. B. The mean of the sample means increases and the standard error increases. C. The mean of the sample means increases and the standard error stays constant. D. The mean of the sample means decreases and the standard error decreases. E. The mean of the sample means increases and the standard error decreases. F. The mean of the sample means stays constant and the standard error increases. G. The mean of the sample means decreases and the standard error stays constant. H. The mean of the sample means decreases and the standard error increases. I. The mean of the sample means stays constant and the standard error stays constant.

f

True or false?: The standard normal distribution has more probability in its tails than the t distribution.

false