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principles of managerial statistics
Questions and Answers of
Principles Of Managerial Statistics
A news show reports that every year a monthly mean of 570 miles of sewer lines are cleaned. Monthly miles of cleaned sewage is reported by the Los Angeles authorities for the Fiscal years of
Write the expressions for H0 and H1.a) The proportion of batteries produced that are defective is no less than 0.05.b) The proportion of houses with solar panels is greater than 0.15.c) The majority
Assuming a Z-test statistic will be used, sketch the rejection region under the test statistic:a) H0 ∶ π = 0.4;H1 ∶ π ≠ 0.4; α = 0.05b) H0 ∶ π ≤ 0.75;H1 ∶ π > 0.75; α = 0.01c) H0
Say thatH0 ∶ π ≥ 0.25H1 ∶ π < 0.25If n = 150 and α = 0.01, compute the p-value and state if you reject the null or not whena) X = 37.b) X = 44.c) X = 12.d) X = 23.
Suppose thatH0 ∶ π ≤ 0.80H1 ∶ π > 0.80If n = 400 and α = 0.05, compute the p-value and state if you reject the null or not whena) X = 315.b) X = 350.c) X = 394.d) X = 320.
Say thatH0 ∶ π = 0.33H1 ∶ π ≠ 0.33If n = 250 and α = 0.10, compute the p-value and state if you reject the null or not when,a) X = 70.b) X = 85.c) X = 83.d) X = 200.
You are the owner of a local women’s clothing store. Blouses, hats, and purses are among some of the items you sell. There are two sort of blouses of a certain brand, regular cut style and skinny
In a survey of 90 participants from the LGBT community from across Riverside and San Bernandino counties in California, 74.4% of respondents indicated that they had seriously considered committing
According to experts, by mid-2016, US shoppers made 51% of their purchases online (Wall Street Journal, June 8, 2016), marking the first time that shoppers made more than half their purchases online.
Interpret the confidence interval in Figure 10.16. Does it support the conclusion reached with the hypothesis test? Test and Cl for One Proportion Test of p = 0.312 vs p < 0.312 Sample X N Sample p
A political candidate claims that from 2008 to 2012 the percentage of people aged 25+ in Chicago without a high school diploma exceeded 25%. Socioeconomic indicators for the city of Chicago during
A political candidate claims that from 2008 to 2012 the percentage of people aged 16+ in Chicago who were unemployed was 15%. Socioeconomic indicators for city of Chicago during this period are
Which statement about the null hypothesis is correct?a) Statement must always have a strict inequality in it (>, <, or ≠).b) It must always say something about the population mean.c)
Which of the following is the correct combination:a) H0 ∶ μ > 25; H1 ∶ μ < 25.b) H0 ∶ μ > 100; H1 ∶ μ ≤ 150.c) H0 ∶ μ ≤ 75; H1 ∶ μ < 75.d) H0 ∶ μ ≤ 300; H1 ∶
Choose the appropriate alternative to go with H0∶ π ≤ 0.42.a) H1 ∶ π > 0.42.b) H1 ∶ π ≠ 0.42.c) H1 ∶ π ≥ 0.42.d) Not possible to tell.
If H0 ∶ μ ≤ 12 is not rejected when the true population mean is 15, determine the best answer below.a) No error was incurred.b) Type I error was incurred.c) Type II error was incurred.d) Both
If H0 ∶ μ ≥ 75 is rejected when the true population mean is 80, determine the best answer below.a) No error was incurred.b) Type I error was incurred.c) Type II error was incurred.d) Both Type I
An employee at a water management agency is studying the daily rainfall for last November at region X. The goal is to determine if the region’s mean daily rainfall from last November was below the
A researcher is claiming that from 2008 to 2012, the per capita income of Chicago residents was $26 000 or less. Socioeconomic indicators during this period for the city of Chicago are available. Use
After many years working at a beauty counter at a department store, Lisa decides to open her own store. She needs to set up a business plan proposal to get a loan from a bank. Her preliminary
Los Angeles authorities are aware that monthly mean residential water usage at the 90007 zip code was 45.14 (measured in hundred cubic feet). Residents in one neighborhood claimed they had always
For a one-sided hypothesis on the population mean, the population is known to follow a normal distribution. While using a small sample size, an analyst chooses a Z statistic as a test statistic by
An administrator believes that the mean proportion of people who carpooled to work in Baltimore from 2008 to 2012 was less than 0.15. Use the data (carpool12) in the file
Officials in Chattanooga, Tennessee are aware that in the past, 12% of their residents own a business. One of the 2016 community survey questions was “do you own a business in Chattanooga?” Out
Suppose San Francisco airport (SFO) administrators have made decisions based on the belief that no more than half of airport visitors make restaurant purchases. According to a 2011 survey, they found
While explaining the results of an analysis to superiors, it comes up that a two-sided hypothesis test was used and the null was rejected. But the superiors are really interested in one direction
A company has designed a new lithium battery. They conducted a study to see if the new battery lasted over two times longer than the average of competitors (μ0) and found that it did. What would be
The power of a test is found to be 0.75.What is the meaning of this?
What is the meaning of the level of significance in hypothesis testing? For example what does 0.05 significance mean?
Analysts for a firm tested if a new computer design allowed to perform high computation algorithms faster than competitors, H0 : μ ≥ 5 versus H0 : μ < 5 (minutes).The analysts argue that since
IfH0 ∶ μ ≤ 2.5H1 ∶ μ > 2.5and during a Z-test, z = 1.44, which of the following best represents the meaning of the p-value? (You may choose more than one if deemed appropriate.)a) P(Z ≤
If t1 follows a t-distribution with 10 degrees of freedom and t2 a t-distribution with 5 degrees of freedom, determine which probability will be greater (no computation necessary).a) P(t2 > 1.12)
In 2013, it was estimated that out of 5395 births in the Australian Capital Territory, the mean rate of perinatal deaths per 1000 babies was 7.6, with a standard error of 1.18. Find a 95% confidence
Download “Minneapolis_Property_Sales_20102013” a data set of property sales in Minneapolis.a) Using statistical software, extract data for transactions such that “PropType = Residential.”b)
Using the data “2014_Housing_Market_Analysis_Data_by_Zip_Code,” produce a scatterplot of “rental units affordable to average artist” and “owner units affordable to average artist” at
Using the data “2014_Housing_Market_Analysis_Data_by_Zip_Code,” produce a scatterplot of “rental units affordable to average teacher” and “owner units affordable to average teacher” at
Recall that a categorical scale with no logical order is known as nominal scale. Explain why for such data, the mode can be used, but not the mean or median.
Suppose we choose 2 balls from a bin with 100 red balls, 100 blue balls, and 100 green balls. If we define R = a red ball is chosen, B = a blue ball is chosen, and G = a green ball is chosen,a) Write
Show that for two independent events A, B, P(B|A) = P(B).
Let A and B be any two events. Assuming P(A) > 0 and P(B) > 0:a) Prove that if A is an event that is independent of B, then A is independent of Bc. Must be proven GENERALLY (IN AN ABSTRACTWAY),
If P(A|B) > P(A), show that P(B|A) > P(B).
If a population follows a normal distribution with mean 10 and standard deviation 2, show thata) If X is the value of a randomly sampled observation from this population, it has an expected value of
Find the standard error of X̅ for each random sampling situation.a) σ = 6, n = 10b) σ = 6, n = 40c) σ = 6, n = 60d) Do you need to assume the population is normally distributed for the
The company BEEFJERK produces 100 g of beef jerky with a mean saturated fat of 10 g and a standard deviation of 0.5 g. Fora) One serving of 100 g, what is the expected value of X̅?b) One serving of
Given a normal population with mean 250 and standard deviation 10,a) Should P(X̅ ≤ 259) be greater or smaller than 0.5?b) For which sample size, n = 30 or n = 20 would P(X̅ ≤ 259)
According to the National Center for Education Statistics, the mean costs (fees, room, and board rates) for a four-year public university in the United States was $15 640 for the 2013–2014 academic
The kilowatt/hour (kWh) generated by a solar system of 12 panels from (12–1 p.m.), during the summer months, has a normal distribution with mean 2.25 and a standard deviation of 0.5. If 10 solar
State in which of these cases it is more reasonable to assume that X̅ follows a normal distribution and explain why or why nota) Sample of size 300 comes from a population with some unknown
Two of your employees are conducting statistical analysis. Each one is working with a random sample of 30. The first employee took the sample from a population with a symmetric distribution. The
Average commute times (in minutes) to work at locations across Oregon are found online. With the variable “COMMUTING TO WORK - Mean travel time to work (minutes),” in the file
A machine produces bolts for construction. The length of the bolts has an expected value of 5 in and a variance of 0.05 in. A random sample of 100 bolts is taken.a) What is the mean (expected value)
If π = 0.20, find the mean and the standard error of p̂ whena) n = 100b) n = 200c) n = 50
Free-throw proportion in basketball is8 the number of free throws made divided by the number of attempts. A player has a 0.86 career free-throw proportion. Explain why any free-throw proportion
Determine if normality can be assumed for p̂ whena) n = 25, π = 0.50b) n = 100, π = 0.97c) n = 1000, π = 0.001d) n = 1500, π = 0.21
An employee from a company’s new products department is conducting research on the number of product parts a machine can assemble in an hour. Unbeknown to him, the population distribution is left
For a population with population mean 50 and standard deviation 7,a) If the population is normally distributed, which sample size would lead to the smallest variance for X̅, n = 100 or n = 300?b) If
A December 2017 CNN article established that life expectancy in the United States, on average, was 78.6. Assume that the standard deviation of life expectancy was 12 years. If a random sample that
It has been stated that the standard error of X̅ is σ/√n. This assumes that the population is infinite. If n is a significant proportion of the population size, N, a finite population correction
A company is about to randomly choose customers to fill surveys evaluating the company’s service. One of the questions asks whether customers will use or recommend the company’s services in the
Mention at least three properties that we want an estimator to have.
Construct a confidence interval for μ using each random sample. Assume X̅ is normally distributed.a) x̅ = 58.5, n = 55, σ = 9.2, 99% confidence.b) x̅ = 11.11, n = 150, σ = 1.25, 90%
In each case, state whether the interpretation of a confidence interval is correct or incorrect. If incorrect, explain why.a) There is a 99% probability that the true mean repair cost for a machine
A 90% confidence interval is built for the population mean using 32 observations.a) How likely is it that the confidence interval includes the sample mean?b) How likely is it that the confidence
A study of the effects of running on a random sample of adults found a 95% confidence interval for the true mean heart rate to be (68.74, 111.14), using a normal approximation procedure (the Z
According to www.fueleconomy.gov, a random sample of seven 2016 Subaru Forester AWD2.5 L, 4 cyl, automatic cars gave a mean of 26.4miles per gallon (MPG). Assume MPG for this vehicle follow a normal
The weight of Holstein cows in a farm has a standard deviation of 66.70 pounds. A random sample of 50 cattle has a mean weight of 1420.90 pounds.a) Why can we assume that the sample mean follows a
A random sample of 40 grass-fed beef prices in the United States gave an average of $3.70 (per pound). If the prices are not highly skewed and historically the standard deviation is $0.70,a)
Show that for a 99% confidence interval, zα∕2 = 2.576.
In the past, a car company had to face a burst of bad publicity when faulty brake parts led to car accidents. They would like to ensure their new car models do not have similar problems. To do so,
A solar power company must determine the sample size to infer on the mean utility bill of residents. From previous studies, it was established that the population standard deviation is 40
A university is concerned with its student’s first year mean GPA. They implement new guidelines in the hopes of improving the overall students performance. To verify the guidelines’
To construct a 99% confidence interval on the MPG of a type of vehicle, researchers are debating whether they want a margin of error of 1, or of 2.a) Which margin of error will require a bigger
If t follows a t-distribution with 10 degrees of freedom, and Z a standard normal distribution, determine which probability will be greater (no computation is necessary).a) P(Z > 1.12) versus P(t
A company is in the early stages of developing an eco-friendly laundry machine that will use less water than the competition. A team has conducted a study to determine the mean number of gallons of
Construct a confidence interval for μ using each random sample. Assume a normally distributed population.a) x̅ = 79.3, n = 12, s = 9.2, 95% confidence.b) x̅ = 5.81, n = 20, s = 0.75, 90%
As an owner of a local accounting firm, you would like to know the mean tax refund people get in your town. This way you can advertise how customers can benefit from your services to get a better
Suppose authorities in Chicago, Illinois, would like to estimate the mean number of days to complete graffiti removal request from private property owners. Weekly mean number of days to complete
In an analysis of a random sample of 75 claims to an insurance company, collision repair costs are found to have a mean of $1386. From previous studies, the standard deviation is known to be $735.a)
According to official Kansas City January 2018 records, the monthly average pay of 16 Accountant II positions was $4053. The minimum pay was $3353 and maximum pay was $5757. Someone would like to use
Construct a confidence interval for π using each random sample and a normal approximation.a) x = 34, n = 55, 95% confidence.b) x = 17, n = 149, 90% confidence.c) x = 214, n = 555, 99% confidence.d)
In Problem 9.24, check for each case if the conditions for a normal approximation hold.Data from in Problem 9.24Construct a confidence interval for π using each random sample and a normal
A 95% confidence interval is built for the population proportion using 200 observations.a) If the chosen confidence level was instead 90%at the same sample size, which confidence interval would be
Suppose the administration at a local university claims that 65% of their college graduates obtain jobs no longer than a month after graduation. For 150 randomly chosen college graduates of the
From the 2013 New York Youth Behavioral Risk Survey, we can be 95% confident that the proportion of youth who drank five or more alcoholic drinks in the past 30 days is between (0.098, 0.118). If a
According to the CDC, in 2015, of 208 595 kids younger than six years old tested for lead in the blood in Massachusetts, 5889 had levels between 5 and 9 μg/dl. Calculate a 95% confidence interval
A reporter wants to gauge the opinion of college undergraduates about legalizing marijuana,a) Using pn = 0.65 (from a similar study), and a 95% confidence level, determine what the sample size is for
Researchers studying criminal domestic violence rates per 100 000 people in country X took a random sample of 39 cities with at least 250 000 residents. Below, a graphical summary is presented.a)
A nonprofit wishes to build a 95% confidence interval on the proportion of uninsured Americans in the United States. In 2010, 16% of Americans had no insurance. In 2016, it was 8.6%.a) If the
To infer on the proportion of new business that fail within five years, it is found that a random sample of 1877 businesses is needed. The boss considers this sample size to be too large and suggests
After much effort, you are convincing your “old school” boss to construct a confidence interval as part of the decision-making process for a new customer service program. Regarding the confidence
A company will conduct an experiment to determine whether the mean time it takes to make a type of earring is within a certain limit. Assuming that the times to make the earrings have a standard
A university is concerned with the second-year student’s mean GPA. They implement new guidelines in the hopes of improving the overall students’ performance. To verify the guidelines’
The Southern California authorities are 95% confident that the rate of people killed in traffic accidents in 2010 was between (4.27, 4.89). Find the point estimate of the rate of people killed.
As part of the decision about opening a new store, the management of a company wanted to infer about the average amount of daily sales the store would have. They knew for a fact that the standard
The owner of an oil change shop would like to know the mean time it takes to do an oil change at the shop. He takes a random sample of 16 cars that were serviced and finds a sample average of 20.5
Current weekly sales of regular ground coffee at a supermarket average 354 pounds and vary according to a normal distribution. The store wants to reduce the price to sell more ground coffee. After
An indicator of the reliability of an estimate is known as the Relative Standard Errors (RSE). RSE = s.e.∕estimate × 100, where s.e. is the standard error of the estimate. In 2013, with 95%
A manufacturer of automobile tires claims that the average number of trouble-free miles given by one line of tires made by his company is 45 000 miles. When 16 randomly picked tires were tested, the
Construct a 99% confidence interval for the true proportion of adolescents in California who consumed five or more servings of fruits and vegetables a day, when in a 2012 random sample of 1143
The spokesperson of a company claims that over 88% of Americans either own a drone or know somebody who does. In a random survey of 1036 Americans, 856 said they or someone they know owned a drone.
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