ECN 221 Final Foster

Use the data below to calculate the coefficient of correlation between x and y. XY 48 29 96 46 49 84 24 32 15 70 18 100 43 67 76 41

-0.4101

Calculate the Z-Score for the observation of 34 using the following dataset and the sample standard deviation. 30, 78, 34, 44, 35, 93, 51, 83, 49 Round your answer to four decimal places.

-0.9054

The average weight of the entire batch of all the bags of candy filled today was 9.98 ounces. A random sample of four bags was selected with the following weights: 11.76, 11.16, 12.51, and 13.12. The sampling error for this sample is: Hint: Do not forget to include sign ROUND TO TWO DECIMALS

-2.1575

Use the data below to calculate the covariance between x and y. XY 50 93 56 13 26 67 75 58 77 3 68 88 78 8 49 50

-284.786 (Sum of X x Y) - (1/8) * (Sum of X x Sum of Y). (##/8-1) = covariance coefficient

Question 35 If you estimate b; to be equal to 3.88, and you have calculated that y-bar (the average of y) is equal to 22.63, and x-bar (the average of x) is equal to 7.81 , then the the value of the constant, bo, is equal to: ROUND TO TWO DECIMAL PLACES

-7.67

Given that z is a standard normal random variable, compute the probability that it takes on a value between -2 and -1.

.1359

Suppose a drug test is 86% sensitive and 87% specific. That is, the test will produce 86% true positive results for drug users and 87% true negative results for non-drug users. Suppose that 4.9% of people are users of the drug. If a randomly selected individual tests positive, what is the probability he or she is a user?

.2542 This is a Bayes' Theorem problem. Think about what A and B are in the formula. We want to know the probability of the person being a drug user, so that is "A". The information we received is that they tested positive, so that is "B".

In a group of 24 boys and 16 girls, three people are chosen at random. What is the probability that 1 girl and 2 boys are selected?

.4470 First, determine how many ways there are to select one girl and two boys from these groups. Remember that in a scenario like this, order does not matter. So we use the to choose 1 girl from the total number of girls and and multiply that by the boys from the total number of boys. Second, determine how many ways there are to select 3 total + girls using the same method. The final probability takes the combinations to choose 2 combinations formula children from the group of boys number of ways we get 1 girl and 2 boys and divides by the number of ways there are to pick 3 children. (24C2 * 16C1) / 40C3

Suppose there are two full bowls of cookies. Bowl #1 has 19 chocolate chip and 30 plain cookies, while bowl #2 has 18 of each. Our friend Fred picks a bowl at random, and then picks a cookie at random. The cookie turns out to be a plain one. What is the probability that Fred picked Bowl #1?

.5505 This is a Bayes' Theorem problem. Think about what A and B are in the formula. We want to know the probability Fred picked bowl 1, so that is "A", and the information we received is that from a random bowl Fred got a plain cookie, so getting a plain cookie is "B". (30/45) / (30/45 + 18/36)

A random variable is normally distributed with a mean of u = 50 and a standard deviation of a = 5. What is the probability that the random variable will assume a value between 45 and 55?

.6826

If the standard error of the mean is 10 years of experience for a sample of consisting of 40 workers, what is the probability that the sample mean will not exceed 22 years for a population with a mean of 17 years experience.

.6915

A random variable is normally distributed with a mean of u = 34 and a standard deviation ofo = 21. Calculate the Z-score for a value of 46.

0.5714

If the population standard deviation is 18 and the population size is 44,312 and the sample size is 787. what is the standard error of the mean? ROUND TO TWO DECIMAL PLACES. Hint: Do you need to use the finite population correction factor?

0.6359

If in a simple regression the following are reported: SSR = Sum of Squares Due to Regression = 3,320.43 SSE = Sum of Squares Due to Error = 256.33 What is the Coefficient of Determination (R2)? YOUR ANSWER SHOULD BE BETWEEN O AND 1. ROUND TO FOUR DECIMAL PLACES

0.9283

Use the data below to calculate the coefficient of correlation between x and y. XY 19 17 35 27 36 36 48 51 43 55 60 63 71 75 99 98 Round your answer to four decimal places.

0.9764

A sample of 13 people has a mean of 51.1 and a standard deviation of 35.78. Calculate the t-statistic for the hypothesis: 4 = 40.5. Round your answer to four decimal places.

1.0682

Use the following information to calculate the t-statistic, X = 42.17 Sx = 28.29 n = 35 Ho : u> 35 Round your answer to four decimal places.

1.4994

Suppose you toss a six-sided die 11 times. What is the probability of never rolling a 6?

1.8333 Each roll of the die is an independent event with a set probability of success, so this would follow the Binomial Distribution. The trick is that a "success" is not rolling a certain number (which happens with a probability of 5/6) and we want all successes.

If a sample of 24 people yields an estimate of 11.11 for b1, what is the upper bound of the 95% confidence interval if the standard error of b, is equal to 1.27? ROUND TO TWO DECIMAL PLACES.

13.74

Use the data below to calculate the covariance between x and y. XY 25 5 29 34 40 48 58 46 63 68 65 71 67 73 99 93 Round your answer to four decimal places.

146.1

A panel of 12 jurors needs to be selected from a group of 18 people. How many different compositions for the jury are possible? Yes, the answer to this question is a really big number.

18,564

A call center receives an average of 18.9 calls per hour. Assuming the number of calls received follows the Poisson distribution, what is the variance in the number of calls per hour?

18.9 The variance of the Poisson distribution is equal to the expect value.

Calculate the range for the following dataset. 78, -67, 61, 30, -93, 19, 63, 42, 91 Round your answer to four decimal places.

184

On average, 3.7 babies are born each day at a local hospital. Assuming the Poisson distribution, what is the probability that no babies are born today?

2.4724 Remember that O! = 1 and that X^0 = 1

The monthly spending on gasoline of a sample of 61 households provided a mean of $127 with a sample standard deviation of $11. The population standard deviation is unknown. Let us provide a 95% confidence interval estimate of the mean electric bill for the population of US households. We will assume this population to be normally distributed. What will the margin of error be for the 95% confidence interval? ROUND TO TWO DECIMAL PLACES Hint: you'll need to find the critical value for t.

2.82

According to the chapter "Probability and Coincidence" by John Allen Paulos, about how many people do you need in a room to have a 50% chance two of them have the same birthday?

23

If you roll two six-sided dice and add the results together, what is the probability you get a sum of 9 or higher?

27.7778 Determine the odds for each outcome equal to or greater than the one given in the question and then add those together.

Calculate the sample standard deviation for the following dataset. 83, 40, 98, 53, 75, 17, 15, 67, 49 Round your answer to four decimal places.

28.4727

Calculate the standard error of a sample mean for a sample with 18 observations where the standard deviation of the population is 13.49. Round your answer to four decimal places.

3.1796

Suppose we gather the following sample: 42 14 18 35 19 10 12 36 30 27 Using this sample, calculate the standard error for the t-statistic.

3.5498

Suppose we gather the following sample: 13 19 18 27 45 49 28 15 43 12 Using this sample, calculate the t-statistic for the hypothesis: u = 10.8.

3.6254

Use the following information to calculate the t-statistic. X = 45.93 Sx = 23.71 n= 40 Hn: u= 31 Round your answer to four decimal places.

3.9825

Suppose we gather the following sample: 31 21 47 18 20 17 40 32 37 13 Using this sample, calculate the upper bound for the 95% confidence interval, Hint: you'l need to find the critical value for t.

35.7502

Calculate the average price of material for the following dataset:

4.72

Calculate the sample mean of the following dataset. 36, 23, 34, 89, 27, 49, 80, 38, 22, 89 Round your answer to four decimal places.

48.7

Calculate the five-number summary for the following data: 62, 37, 42, 15, 47, 66, 71, 9, 54, 56, 59, 66 Report the value for the median. In or to determine the five-number summary, you must put these numbers in order.

55

Calculate the mode of the following dataset. 16, 41, 55, 55, 18, 68, 55, 74 Round your answer to four decimal places.

55

Suppose that I flip a fair coin 33 times. What is the probability that it will land on heads exactly 19 times?

57.5758 Flipping a coin n times would follow a binomial distribution where p is 0.5 and a "success" is getting "heads".

Calculate the sample mean of the following dataset. 49, 38, 48, 83, 76, 90, 56, 42 Round your answer to four decimal places.

60.25

Each year a restaurant selects a simple random sample of 380 corporate customers in their dining rewards program in order to learn about amount they spend. The historical data indicates that the population follows a normal distribution. Last year, they monitored 380 corporate customers (n %3D = 380) and obtained a sample mean of (x )= $19,130. Based on historical data, they now assume a known value of o = $619. The confidence coefficient to be used in the interval estimate is .95. What will the margin of error be for for their 95% confidence interval? ROUND TO TWO DECIMAL PLACES

62.24

Calculate the sample coefficient of variation for the following dataset. 40, 58, 7, 77, 99, 85, 63, 17, 12 Don't forget to multiply by 100 to put in percentage terms. Round your answer to four decimal places.

66.1402

How many ways are there to arrange 6 people in a line-up?

720

Calculate the five-number summary for the following data: 60, 87, 70, 75, 8, 38, 71, 48, 68, 61, 91, 68 Report the value for Q3. In or to determine the five-number summary, you must put these numbers in order.

8, 54, 68, 73, 91

A previous study that cost of a certificate in a certain programming language was $1,066 with a population standard deviation of $161. Suppose the developer of a new certificate wants estimate of the population mean birthing cost such that there is a .95 probability that the sampling error is $35 or less. How large a sample size is needed to meet the required precision? ROUND TO TWO DECIMALS (EVEN THOUGH IT DOESNT MAKE SENSE)

81.29

A recent survey found that 81.6% of households has Internet access and 84.4% of households had cable television. Also, it was reported that 73.0% of households had both Internet access and cable television. Determine the probability that a randomly selected household in the survey had either Internet access or cable.

93 Remember the General Addition Rule: P(A or B) = P(A) + P(B) - P(A and B). Here A would be having internet access, and B would be having cable television.

Calculate the five-number summary for the following data: 7, 74, 96, 20, 20, 73, 50, 85, 5, 37, 25, 15 Report the value for the maximum. In or to determine the five-number summary, you must put these numbers in order.

96

Which of the following is the deterministic component in the standard single equation linear model?

B0 + B1

The null and alternative hypotheses must:

Be fully exhaustive and have no elements in their union

The binomial probability function contains a portion that represents a:

Combination of certain outcomes

Which of the following is the stochastic component in the standard single equation linear model?

E

The Ordinary Least Squares method of regression focuses on minimizing the:

Error, squared sum of errors or SSE

A data dashboard CANNOT show information about both categorical and quantitative data.

False

Induction reasons from the general to the specific.

False

Mathematical proofs, like those in geometry, use the inductive method of reasoning.

False

The degrees of freedom are used to determine the critical z-score for the normal distribution when calculating a confidence interval.

False

The margin of error can be reduced by reducing the size of the sample

False

The number of independent variables in a multiple regression can be greater than the number of observations.

False

The number of values a discrete random variable may assume must be finite.

False

The probability for a given range of a continuous random variable can be calculated by measuring the slope of the density function in that range.

False

Type I errors are always preferred to Type II errors.

False

Type Il errors are always preferred to Type I errors.

False

When determining the sample size required for a 95% confidence interval for the population mean, the sample mean needs to be known.

False

An estimated regression line which shows no real relationship between two variables is:

Horizontal

Metaphors created to compare the world to something abstract are known as

Models

What level of measurement would political party be (e.g. choice of Democrat, Republican, Independent, or Other)?

Nominal

What level of measurement would year in school be (e.g. first year, second year, third vear, or fourth year and above)?

Ordinal

Which of the following would be the BEST example of panel data?

Red blood cell count for every member of a controlled trial every month over the course of a year

Which of the following represents the probability that any given confidence interval will not contain the true population mean?

Significance level

Which is a measure of the variability of the middle 50% of a given data set?

The interquartile range

Which of the following is NOT a characteristic of a binomial experiment?

The probability of a success must exceed the probability of a failure.

Attempts to describe the principles that drive the world are known as

Theories

A one-tailed test can occur when the null hypothesis assumes the true population mean is greater than or equal to some value OR less than or equal to some value.

True

A regression cannot under any circumstances prove causality.

True

A scatter diagram requires that both variables must be quantitative in nature.

True

Deduction reasons from the specific to the general.

True

In a regression estimation the residual can be observed, but the error term cannot be observed.

True

In a simple regression with one independent variable the error term is assumed to have the same variance for all values of the independent variable.

True

Mutually exclusive events may not have sample points in common.

True

One of the often overlooked costs of data acquisition are the errors that exist in easily or hastily collected data

True

The sum of all the z-scores for each observation in a given population data set can be positive or negative.

True

The sum of the probabilities for all possible experimental outcomes must equal one.

True

To truly be a census, data must be collected for the entire population.

True

Z-scores can only be used to calculate probabilities based on standard errors of the mean, NOT standard errors of the proportion.

True

Which of the following is the dependent variable in the standard single equation linear model?

Y

State which of the fallacies below BEST describes the following argument: That guy was an awful athlete. Sure he broke records, but he broke the heart of his wife and kids when he started a second secret family.

ad hominem

State which of the fallacies below BEST describes the following argument: More and more people have stated that the moon landing was a fake. I am starting to believe it.

bandwagon fallacy

State which of the fallacies below BEST describes the following argument: Nixon refused to wear makeup for the first televised debate against Kennedy. He looked terrible. It cost him the election.

bandwagon fallacy / appeal to authority / anecdotal evidence / the narrative fallacy ??

An exponential probability function with an expected population value of one will have a density function of:

f(x)=1/e

What type of statement is the sentence below? The same side of the moon always faces the earth because it is tidally locked.

objective

Increasing the sample size when calculating a confidence interval while keeping the confidence level constant will:

reduce the margin of error resulting in a narrower (more precise) confidence interval.

Normativism is:

subjective.

The coefficient of determination is equal to:

the sum of squares due to regression divided by the total sum of squares

What type of data would we have if we collected the price of a given stock everyday for a month?

time series data

The ___ of events A and B is the event containing all sample points that are in A or B or both.

union

Suppose we gather the following sample: 36 25 20 24 19 13 14 28 22 42 Using this sample, calculate the upper bound for the 95% confidence interval. Hint: you'll need to find the critical value for t. Round your answer to four decimal places

зо взоз