Econ exam solutions

For a particular clothing store, a marketing firm finds that 28% of $10-off coupons delivered by mail are redeemed. Suppose that 16 customers are randomly selected and are mailed $10-off coupons. FYI: BINOM.DIST(number of successes, trials, probability of success, cumulative) What is the probability that five or fewer customers redeem the coupon? a) BINOM.DIST(4, 16, 0.28, True) b) BINOM.DIST(5, 16, 0.28, True) c) 1- BINOM.DIST(4, 16, 0.78, True) d) 1 - BINOM.DIST(5, 16, 0.28, False)

BINOM.DIST(5, 16, 0.28, True)

Suppose the dealer incentive per vehicle for Honda's Acura brand is thought to be bell-shaped and symmetrical with a mean of $2,500 and a standard deviation of $300. Based on this information, what interval of dealer incentives would we expect approximately 95% of vehicles to fall within? [Hint: Think of EmpiricalRule] a) $2,200 to $2,800 b) $1,600 to $3,400 c) $1,300 to $3,700 d) $1,900 to $3,100

$1,900 to $3,100

the cumulative relative frequency of "10-19 number of hours" is 0.25. this means that a. 25% of students have a number of hours worked above 19 hours b. 25% of students have a number of hours worked below 10 hours c. 25% of students have a number of hours worked below 19 hours d. 25% of students have a number of hours worked between 10 and 19 hours

25% of students have a number of hours worked below 19 hours

Which of the following represents an appropriate set of hypotheses? a) H0: p≠0.45, H1: p=0.45 b) H0: 𝑥≥0.8, H1: 𝑥<0.8 c) H0: μ≥0.55, H1: μ<0.55 d) H0: μ≤156, H1: μ>254

H0: μ≥0.55, H1: μ<0.55

data represents a sample of ten students and their preferences for ice cream suppose you are asked to construct a frequency distribution of preferred ice cream flavors with this dataset. what are the most appropriate classes/bins? a. 1.999, 3.999, 5.999, 7.999, 9.999 b. strawberry, vanilla, chocolate, coconut, pistachio c. strawberry, vanilla, chocolate d. maria, john, julie, anny, nick, alex

strawberry, vanilla, chocolate, coconut, pistachio

Refer to Exhibit Influenza. What is the probability that the average number of missed days for the sample of 16 students is between 25 and 31? a) 0.9544 b) 0.6306 c) 0.5 d) cannot be determined

cannot be determined

You want to know about the mean price of gas per gallon in Indiana, so you are going to select 30random gas stations in Indiana. With the information given below, answer the following questions.• P(z < 1.96) = 0.975 and P(z < 1.645) = 0.95 where z follows the standard normal distribution.• P(t < 2.045) = 0.975 and P(t < 1.699) = 0.95 where t follows the student t's distribution with the degree of freedom, 29 Suppose you know the population standard deviation as $0.50. What is the margin of error for the 95% confidence interval for the population mean price of gasper gallon? a) 0.1502 b) 0.1789 c) 0.1658 d) 0.9801

0.1789

Question 4) Refer to the Exhibit Prevalence Rate. The sample collected for the study had the following distribution of age across different age groups (bounds are inclusive for the interval representing an age group ): What is the cumulative relative frequency for the class 5-18 years? a. 0.1655 b. 0.0212 c. 0.1867 d. 0.2570

0.1867

You want to know about the mean price of gas per gallon in Indiana, so you are going to select 30random gas stations in Indiana. With the information given below, answer the following questions.• P(z < 1.96) = 0.975 and P(z < 1.645) = 0.95 where z follows the standard normal distribution.• P(t < 2.045) = 0.975 and P(t < 1.699) = 0.95 where t follows the student t's distribution with the degree of freedom, 29 suppose you do not know the population standard deviation. Therefore, you instead calculated the sample standard deviation from the sample, and it was$ 0.85. What is the margin of error for a 95% confidence interval for the population mean price of gasper gallon? a) 0.2553 b) 0.2637 c) 0.3042 d) 0.3174

0.3174

Refer to Exhibit Influenza. Assuming that the number of missed days in the population follows the normal distribution, what is the probability that a randomly selected student missed 31 days or more? Calculate the value using the table. P(x > 31) = P(z > 3/9) a) 0.6306 b) 0.3694 c) 0.0228 d) Cannot be determined

0.3694

The percentage of companies that use social media tools and technologies has been increasing over the past several years. A random sample of 160 companies found that 80 of them use social media tools and technologies. Determine the UPPER bound of the 99% confidence interval for the proportion of companies using social media tools. Round your answer to 4 decimal places. Choose an appropriate critical value given below to calculate the upper bound. 𝑧0.005= 2.5758, 𝑧0.01 = 2.3263, 𝑡0.005 = 2.6052, 𝑡0.01 = 2.3486 a) 0.4099 b) 0.6018 c) 0.4001 d) 0.5988

0.6018

According to Orangetheory Fitness, 37% of the registered members participated in a new advertised program. A random sample of 70 registered members was selected. What is the probability that more than 30% but less than 45% of members in the sample participated in the new program? Please, consult the following table to perform calculations: a. 0.9081 b. 0.8605 c. 0.8046 d. Cannot be determined using the above table

0.8046

For a particular clothing store, a marketing firm finds that 28% of $10-off coupons delivered by mail are redeemed. Suppose that 16 customers are randomly selected and are mailed $10-off coupons. FYI: BINOM.DIST(number of successes, trials, probability of success, cumulative) Question 23) What is the probability that more than 8 customers redeem the coupon? a) BINOM.DIST(8, 16, 0.78, True) b) 1- BINOM.DIST(8, 16, 0.28, True) c) BINOM.DIST(7, 16, 0.28, True) d) 1- BINOM.DIST(7, 16, 0.28, True)

1- BINOM.DIST(8, 16, 0.28, True)

For a particular clothing store, a marketing firm finds that 28% of $10-off coupons delivered by mail are redeemed. Suppose that 16 customers are randomly selected and are mailed $10-off coupons. FYI: BINOM.DIST(number of successes, trials, probability of success, cumulative) What is the standard deviation of the number of coupons that will be redeemed? a) 3.2256 b) 1.7960 c) 4.79 d) 2.1166

1.7960

A portion of a table below shows an example of a dataset recording the number of text messages sent over one day by teenagers in a sample. Sample data is summarized in the histogram which is also displayed below: Which of the following would be the best interpretation of the frequency displayed in the first bar on the left(circled)? Hint: it might be helpful to think about axes labels first. a. 5 teenagers sent 3 messages during the day b. 3rd teenager in a sample sent 5 text messages during the day c. 3 teenagers sent 5 messages during the day d. 3rd teenager was observed for 5 days and has 5 data values associated with him in the data set

5 teenagers sent 3 messages during the day

Refer to the Exhibit Serial Interval for COVID-19. Assume that a sample of COVID-19 patients was taken and the serial interval at the 60th percentile is equal to 3 days. Which of the following statements best interprets this finding? a) 60% of individuals in the sample started developing symptoms in less than 3 days after the primary case b) Most frequent serial interval for the bottom 60% of patients is equal to 3 days c) The average of bottom 60% of serial intervals equals 3 days d) Middle 60% of cases in the sample had an average serial interval of 3 days

60% of individuals in the sample started developing symptoms in less than 3 days after the primary case

when interpreting the correlation coefficient between variable x and y, which of the following statements is the most accurate and complete? a. A value of the correlation coefficient equal to -0.1 indicates that, on average, as x decreases, then y tends to decrease. Additionally, the relationship is strong between these two variables. b. A value of the correlation coefficient equal to -0.1 indicates that, on average, as x increases, then y tends to decrease. Additionally, the relationship is weak between these two variables. c. A value of the correlation coefficient equal to 0.9 indicates that, on average, as x increases, then y tends to increase. Additionally, the relationship is weak between these two variables. d. A value of the correlation coefficient equal to 0.9 indicates that, on average, as x increases, then y tendsto decrease. Additionally, the relationship is strong between these two variables.

A value of the correlation coefficient equal to -0.1 indicates that, on average, as x increases, then y tends to decrease. Additionally, the relationship is weak between these two variables.

an analyst gathered the following information about the net profit margins of companies in two industries: compared with the other industry, which industry has more consistent net profit margins? in other words, which industry has a smaller relative variation of net profit margins? a. A, because it has a smaller range b. B, because it has a smaller standard deviation c. B, because it has a smaller mean d. A, because it has a smaller coefficient of variation

A, because it has a smaller coefficient of variation

According to Orangetheory Fitness, 37% of the registered members participated in a new advertised program. A random sample of 70 registered members was selected. What is the shape of the sampling distribution of the proportion of members participated in the new program? a. Can be any distribution because the population distribution is not specified in the problem. b. Normal because the n > 30 and the CLT applies. c. Student's t-distribution because the population standard deviation is not known. d. Can be approximated by a normal distribution because np ≥ 5 and nq ≥ 5

Can be approximated by a normal distribution because np ≥ 5 and nq ≥ 5

The following chart shows two scatter plots in one graph. One is between X and Y1, and the other is between X and Y2. The x-axis represents X, and y-axis represents both Y1 and Y2. Which of the following is false? a) Correlation coefficient between X and Y1 and the one between X and Y2 are same as 1. b) Correlation coefficient is greater between X and Y2 than the one between X and Y1 because the slope is higher between X and Y2. c) Correlation coefficient between Y1 and Y2 will be positive. d) X has positive covariance with both Y1 and Y2.

Correlation coefficient is greater between X and Y2 than the one between X and Y1 because the slope is higher between X and Y2.

Which of the following experiments does not generate a continuous random variable? a) Measuring the number of ounces of soda in a bottle b) Recording the number of minutes a customer waits on hold for technical support c) Counting the number of customers who enter a store during the business day d) Recording the number of miles traveled between two locations

Counting the number of customers who enter a store during the business day

The waiting time for customers at MacBurger Restaurants follows the normal distribution.At the Warren Road MacBurger, the quality-assurance department sampled 25 customers and found that the mean waiting time in the sample was 2.62 minutes and the sample standard deviation was equal to 1 minute. You conduct a test to verify if the mean waiting time is lower than 3 minutes and find that the p-value for the test is 0.1001. The p-value is best interpreted as the following: a) If, in fact, the average waiting time for customers at MacBurger Restaurants is 3 minutes, then there is a 10.01% probability of observing the average waiting time in the sample of 25 customers equal toor less than 3 minutes. b) There is a 10.01% probability of observing the average waiting time in the sample of 25 customers equal to or less than 2.62 minutes. c) There is a 10.01% probability that the average waiting time for customers at MacBur

If, in fact, the average waiting time for customers at MacBurger Restaurants is 3 minutes, then there is a 10.01% probability of observing the average waiting time in the sample of 25 customers equal toor less than 2.62 minutes

A statistician found out her estimation of confidence interval is meaningless because thewidth of the interval is too wide. Which of the following do you think is the best recommendation? a) Decrease the sample size b) Increase the level of confidence for the interval c) Reduce the sample variance d) Increase the sample size

Increase the sample size

Which of the following statements is the most accurate about a binomial random variable? a) The binomial random variable does not have a probability distribution b) The outcome of each trial is a fixed number c) It is a continuous random variable d) It counts the number of successes in a given number of trials

It counts the number of successes in a given number of trials

According to Orangetheory Fitness, 37% of the registered members participated in a new advertised program. A random sample of 70 registered members was selected. What are the mean and the standard error of the sampling distribution of the proportion of members participated in the new program when a sample of70 members is used? a. Mean = 25.9. Standard error = 4.0394 b. Mean = 0.37. Standard error = 0.0577 c. Mean = 25.9. Standard error = 5.0892 d. Mean = 0.37. Standard error = 0.0442

Mean = 0.37. Standard error = 0.0577

Last year, 50% of MNM, Inc. employees were female. It is believed that there has been a reduction in the percentage of females in the company. This year, in a random sample of 380 employees, 170 were female. Based on this information, you want to determine if there has been a decrease in the percentage of females in the company (at the significance level of 5%). Suppose you decided to use the p-value approach. Calculate the p-value for the test. a) NORM.S.DIST(-2.0634,TRUE) b) 1-NORM.S.DIST(-2.0520,TRUE) c) NORM.S.DIST(-2.0520, TRUE) d) None of the above

NORM.S.DIST(-2.0520, TRUE)

A city is considering widening a busy intersection in town and is interested to determine whether the intersection has seen an increase in traffic this year. Last year, the city reported 16,000 cars passed through the intersection per day. This year, the city collected information for the sample of 38 days and found an average of 17,000 cars passed through the intersection. Historically, the population standard deviation of the number of cars passed through the intersection per day has been 5,000. Choose an excel function to find an appropriate critical value to test council's belief at a 15% significance level. a) NORM.S.INV(0.15) b) NORM.S.INV(0.85) c) T.INV(0.15, 37) d) T.INV(0.85,37)

NORM.S.INV(0.85)

Which of the following is not true regarding the normal distribution of random variable X with mean 𝜇 and standard deviation 𝜎? a. Smaller 𝜎 results in a flatter curve that is more spread out around the mean and not as tall. b) The mean of X = The median of X c) If 𝜇 and 𝜎 are known, we can calculate any probability of X. d) 𝑃(𝑋 < 𝜇 ― 𝜎) = 𝑃(𝑋 ≥ 𝜇 + 𝜎)

Smaller 𝜎 results in a flatter curve that is more spread out around the mean and not as tall.

Assume that a sample of COVID-19 patients was taken and the z-score for the serial interval of one patient inthe sample equals 0.75. This z-score is best interpreted as: a) The serial interval for this patient is 0.75 standard deviations above the average serial interval in the sample. b) The serial interval for this patient is 0.75 days above the average serial interval in the sample. c) Standard deviation of the serial interval is 0.75 days above the serial interval for this patient. d) 75% of patients show a serial interval above this patient

The serial interval for this patient is 0.75 standard deviations above the average serial interval in the sample.

Suppose that a 90% confidence interval for the average amount spent annually on a debit card was calculated to be between $7,707.76 and $7,872.24. Which of the followings is INCORRECT about this confidence interval? a. If we took many random samples and from each computed a 90% confidence interval, approximately 10% of these intervals would not contain the population average amount spent on a debit card. b. There is a 90% probability that the population average amount spent on a debit card falls between $7,707.76 and $7,872.24. c. If we took many random samples and from each computed a 90% confidence interval, approximately 90% of these intervals would contain the population average amount spent on a debit card. d. Population average amount spent on a debit card is an unknown but constant number. So, it is either within the confidence interval or not.

There is a 90% probability that the population average amount spent on a debit card falls between $7,707.76 and $7,872.24.

Which of the followings is NOT TRUE regarding confidence intervals? a. When using a sample standard deviation to obtain a confidence interval for the population mean, we can no longer rely on the normal distribution to calculate the critical value. b. A bigger margin of error implies a wider confidence interval. c. When the confidence level increases, the significance level must decrease. d. When we use the Student's t-distribution to find a confidence interval for the mean, we do not need to have sample size greater than 30 or a normally distributed population data

When we use the Student's t-distribution to find a confidence interval for the mean, we do not need to have sample size greater than 30 or a normally distributed population data

Bob's golf score at his local course follows the normal distribution with a mean of 92.1 and a standard deviation of 3.8. The interval around the mean that contains 95% of Bob's golf scores is _______________.(Hint: 𝑃( ―2 < 𝑧 < 2) = 0.95) a) [90.2, 94] b) [88.3, 95.9] c) [84.5, 99.7] d) [80.7, 103.5]

[84.5, 99.7]

which of the following is FALSE about the sample standard deviation as a measure of variability? a. sample standard deviation is impacted by outliers in a data set b. the squared sample standard deviation is equal to the sample variance of the data set c. a data set with higher sample standard deviation always also has a higher coefficient of variation d. the unit of sample standard deviation is same with one of the original data

a data set with higher sample standard deviation always also has a higher coefficient of variation

Over the entire six years that students attend an Ohio elementary school, they are absent, on average,28 days due to influenza. Assume that the standard deviation of the number of days they are absent over this time period is σ = 9 days. Refer to Exhibit Influenza. Upon graduation from elementary school, a random sample of 36 students is taken and asked how many days of school they missed due to influenza. What is the probability that the sample mean is less than 25? To answer the question, consult the following table a) 0.0228 b) 0.9544 c) 0.3694 d) 0.9772

a) 0.0228

The mean of the sampling distribution is always ______ the population mean, and the standard error of the mean is always _______ the population standard deviation except the case where the sample size is equal to _______. Which of the followings fits best in the blanks? a) equal to, less than, 30 b) less than, less than, 1 c) equal to, greater than, 30 d) equal to, less than, 1

equal to, less than, 1

Question 3) Refer to the Exhibit Prevalence Rate. Discussing results of the study conducted with a sample of 3,330 participants, researchers made projections of the prevalence rate for the population of Monroe County using several different methods and were able to conclude that the prevalence of COVID-19 antibodies in Monroe County was between 2.49% and 4.16% by early April (depending on a method).This statement is an example of a/an: a. coefficient of variation b. inferential statistic c. covariance d. descriptive statistic

inferential statistic

Refer to the Exhibit Serial Interval for COVID-19. Assume that a sample of COVID-19 patients was taken and the ______ serial interval in the sample is equal to 2.5 days. The finding is interpreted as "50% of individuals in the sample started developing symptoms in less than 2.5 days after the primary case". What will be the best answer for the blank? a) Mean b) Median c) Mode d) Range

median

a telephone number is an example of BLANK data a. ordinal b. nominal c. quantitative data d. interval

nominal

Which of the following would be required for creating confidence intervals for the population proportion? a) the population must be normally distributed b) the population should be infinite c) np ≥ 5 and n(1-p) ≥ 5 d) the population standard deviation should be known

np ≥ 5 and n(1-p) ≥ 5

Which of the following is NOT true? a. primary data is the data you collected for your own use b. primary data is readily available c. secondary data has no control over how the data was collected d. a researcher needs to check the reliability of secondary data before employing it

primary data is readily available

in december of 2021, it was extraordinarily warm for five days. the rest of the days were similarly cold as the previous year. if given daily temp. data in december 2021, BLANK will be higher than BLANK. if you draw a distribution, it will be BLANK a. median, sample mean, left-skewed b. range, sample variance, right-skewed c. sample mean, cofefficient of variation, left-skewed d. sample mean, median, right-skewed

sample mean, median, right-skewed

Addressing COVID-19 is a pressing health and social concern. A group of researchers from Stanford University conducted research in early April, 2020, to measure the prevalence of antibodies to COVID-19 in the population of Monroe County. Essentially, their goal was to collect evidence of an immune response to the virus in the population, even in people with no symptoms or those who have already recovered from the disease. Their research generated a lot of interest because it would help the scientific community to gain insight into the true infection rate and answer questions about things like asymptomatic spread and how long antibodies last. Question 1) Refer to the Exhibit Prevalence Rate. Researchers recruited a sample of 3,330 people from residents of Monroe County. They found that the prevalence rate of antibodies or the percentage of people who showed the presence of antibodies in the sample is 1.5%. This perce

statistics

scatter plot represents monthly data of US consumer price index and unemployment rate, respectively which of the following is NOT true? a. correlation coefficient calculated with this data is negative b. sample covariance calculated with this data is negative c. the coefficient of variation calculated based on this data will show presence of a strong relationship d. in this graph, the CPI is the independent variable and the UR is the dependent variable

the coefficient of variation calculated based on this data will show presence of a strong relationship

In a recent survey of 500 adults, 18% indicated that they had fallen asleep in front of the television in the past month. Using this data, a 95% confidence interval is constructed for the population proportion of individuals who tend to fall asleep in front of the TV. If you are asked to construct a 99%confidence interval instead, then: a) the margin of error will decrease, and the confidence interval will become narrower b) the margin of error will increase, and the confidence interval will become narrower c) the margin of error will increase, and the confidence interval will become wider d) the margin of error will decrease, and the confidence interval will become wider

the margin of error will increase, and the confidence interval will become wider

which of the following is an example of a binomially distributed random variable? a. the waiting time for a checkout in the grocery store b. the number of students in the classroom c. number of daily visitors to brown county state park d. the number of adults who have a four-year college degree in a sample of 30 adults

the number of adults who have a four-year college degree in a sample of 30 adults

The sampling distribution of the proportion means a) the probability distribution of all possible values of the population proportion (𝑝) b) the probability distribution of all possible values of the original random variable (𝑥) c) the probability distribution of the possible numbers of failures in the sample of size n d) the probability distribution of all possible values of the sample proportion (𝑝)

the probability distribution of all possible values of the sample proportion (𝑝)

Which of the following is TRUE about measures of central tendency? a. if a frequency distribution has three highest peaks of the same height, this implies there is no mode for the data b. they do not show how much spread is present in the data c. the median is the value that appears most often in a dataset d. the population mean is always greater than the sample mean

they do not show how much spread is present in the data

data shows stock price for FaceBook at the end of the past four quarters which of the following data types best describe these values? a. nominal b. time-series c. cross-sectional d. ordinal

time series

The Central Limit Theorem (CLT) states that the sample means. a) cannot be normally distributed if the sample size is too small. b) of any samples will be normally distributed regardless of the shape of their population distributions .c) will be normally distributed as long as the sample is large enough (more than 30) even if the population does not follow normal. d) of large-sized samples will become closer to the true parameter.

will be normally distributed as long as the sample is large enough (more than 30) even if the population does not follow normal.

Refer to the Exhibit Prevalence Rate. The sample distribution meaningfully deviated from that of the Santa Clara County population along several dimensions. To be able to match sample results to the composition of the population of Santa Clara County, researchers collected data on the socio-demographic characteristics of participants in the sample.Which of the following characteristics is an example of qualitative data? a. zip code b. number of people in the household c. age d. years of education

zipcode