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principles of managerial statistics
Questions and Answers of
Principles Of Managerial Statistics
Every year, administrators of the San Francisco airport conduct a survey to analyze guest satisfaction. Suppose management wants to compare the restaurant quality scores of four terminals. Restaurant
Are drone owners in Edmonton, Canada, less concerned than people who do not own a drone about safety with drones flying over people? In a survey to gather community insight about drones, participants
With the help of Minitab, and using the data set “2011_SFO_Customer_Survey,” first subset the rows by whether respondents made a restaurant purchase (“Q4C” = 1). Second, exclude rows where
Is concern about safety with drones, flying over people, related to age? A survey was conducted in Edmonton, Canada, to gather community insight about drones. Participants provided feedback on “I
Returning to Problem 11.35, if the difference is defined as superhero violent events per hour minus villain violent events per hour, use the Minitab output below to answer the following questions at
Enrollment data of schools in Connecticut for the 2013–2014 school year are available in the file “School_Enrollment_Connecticut.” Note that the last row is for all of Connecticut and thus must
From the file “Baltimore_Arts” get the number of art-related businesses per 1000 residents for Baltimore in 2011 and 2012 (artbus11 and artbus12 respectively).a) Perform a paired t-test at 5%
Download Baltimore education data: “BaltimoreEducation_and_Youth__2010-2012_”a) Perform a two mean test at 5% significance to determine if the expected proportion of students receiving free or
An analyst at the firm you work in was comparing the proportions from two independent samples. He was able to use a normal approximation and build a confidence interval for each proportion. Since
Who is more violent, superheroes or villains? A CNN article reported on a research presentation on the matter. The research considered (a random sample) of 10 movies and evaluated the number of
A professor has two possible routes to get to work from home. The distances are not the same but for her it is all about getting to work faster. She has tried both routes, but finds it hard to tell
Inference is needed on the difference between the mean math SAT score of high school students who went to a 10-minute presentation (μ1, group A) and the mean math SAT score of high school students
Have you ever wondered if the proportion of high school students that smoked cigarettes in the past 30 days is different for Hispanics and Whites? Perform a hypothesis test to check if this was the
Ten people participated in a taste experiment to determine if there is a difference in the mean score of two cereals (where 100 is best).a) Write the null and alternative hypothesis.b) What is the
You work for an insurance firm and you must choose between two companies to handle your employer’s investment portfolio. Although both companies have claims about the mean 1-year return for a $10
A company’s data analyst performed a two sample t-test to compare the mean time to pack some jewelry using two separate machines. Curious, a manager asks the analyst if he used an equal variance
A new machine was purchased to can tuna. With the old machine, a random sample of 16 cans revealed an average weight of 6.83 oz and a standard deviation of 0.64 oz. In an independent random sample
Enrollment data of schools in Connecticut for the 2013–2014 school year are available in the file “School_Enrollment_Connecticut” α = 0.10. Note that the last row is for all of Connecticut and
A realtor wants to compare asking prices per square foot for land in neighborhood 1 and neighborhood 2. He takes a random sample of 16 listings from neighborhood 1. From neighborhood 2, a random
In the 2016 General Social Survey, one question was “What is the ideal number of children for a family to have?” Of the 738 men who answered, the mean response was 2.52 with a standard deviation
For a new car model from Company M, engineers proposed a slight tweak in the engine design that could lead to better fuel efficiency. To test this, 10 cars were randomly assigned the originally
If H0 ∶ μ1 − μ2 ≤ 0; H1 ∶ μ1 − μ2 > 0, which of the following is an equivalent statement? (More than one choice is possible.)a) H0 ∶ μ1 − μ2 < 0; H1 ∶ μ1 − μ2 ≥ 0b)
If H0 ∶ μ1 − μ2 ≥ 0; H1 ∶ μ1 − μ2 < 0, which of the following is an equivalent statement? (More than one choice is possible.)a) H0 ∶ μ1 − μ2 < 0; H1 ∶ μ1 − μ2 ≥
If X̅1 = 17.50, n1 = 100, σ1 = 2.07, X̅2 = 10.15, n2 = 100, and σ2 = 1.25.a) Construct a two-sided 90% confidence interval for μ1 − μ2.b) Interpret the confidence interval.
If X̅1 = 199.61, n1 = 75, σ21 = 25, X̅2 = 203.27, n2 = 75, and σ22 = 25.a) Construct a two-sided 90% confidence interval for μ1 − μ2.b) Interpret the confidence interval.
Find the standard deviation of X̅1 - X̅2 whena) n1 = 115, σ1 = 37, n2 = 88, σ2 = 52.b) n1 = 33, σ1 = 61, n2, = 94, σ2 = 59.
Find the standard deviation of X̅1 - X̅2 whena) n1 = 50, σ21 = 25, n2 = 65, σ22 = 25.b) n1 = 200, σ21 = 100, n2, = 150, σ22 = 47.
If you were given the regression equation Ŷ = 4 + 500x and told that since the slope is 500 there is a strong linear association between the two variables, what would you say?
A popular way to measure the volatility of a financial asset, such as a stock, is its beta value. If Y = daily return of an asset, and X = daily return of the S&P 500 index fund (the market),
A new analyst has been hired and you have been asked to take him under your wing. To get things started, you ask him to check if there is an association between two variables X and Y. After a few
In the figures below, determine if the estimated slope of a simple linear regression line will be negative, positive, or close to zero. (a) Y (d) lo 00 Soo 000
If Ŷ = 3.5 − 7.34X,a) Interpret the value of the slope.b) Estimate the mean of the response variable when x = 10.25.
If Ŷ = −0.5 + 11.6X,a) Interpret the value of the slope.b) Estimate the mean of the response variable when x = 0.48.
When β1 = −105.41, what happens to the response variable as X increases?
When β1 = 12, what happens to the response variable as X increases?
If Y = −245 + 71.4X, is the association between Y,X positive, negative, or neither?
If Y = 10 − 43X, is the association between Y,X positive, negative, or neither?
One thing about ANOVA is that the larger the sample size, the greater the power. Does this mean that if n is large enough, ANOVA will detect differences that are false? Explain.
You run a two-way ANOVA at 5% significance and find an interaction effect between Factor A and Factor B. While presenting your results to management, it turns out that your competitive cubicle
A company is going through some tough times. Some executives have recommended closing down one of its four customer centers. The four centers have equal expenses, so management decides to assess mean
One of the best success stories in big data is the use of statistical algorithms to translate text from one language to another. In an attempt to tap this market, a company will assess three
Assume the same amount of observations were collected for each combination of levels of two factors. From the interaction plot below, answer the followinga) How many levels does factor A have?b) How
Fill the blanks in the ANOVA table below: Source DF SS Factor A 4 Error Total | 40 113.12 737.69 MS F P-value 0.188
Refer to the partial ANOVA table below.a) Fill in the missing values.b) Howmany levels does the factor have?c) How many observations were used?d) What is the estimated variance of the response
Refer to the partial ANOVA table below, obtained from an experiment where a total of 16 observations were made.a) Fill in the missing values.b) How many levels does the factor have?c) What is the
Course grades in business statistics are obtained from five randomly chosen students from five different programs. Use Minitab to determine if the data shows significant difference in means at 5%
Using the ANOVA table below at 5% significancea) Is the interaction statistically significant?b) Is factor B relevant?c) Is factor A relevant? Source Factor A Factor B Interaction Error DF
Using the ANOVA table below at 5% significancea) Is the interaction statistically significant?b) Is factor B relevant?c) Is factor A relevant? Source Factor A Factor B Interaction Error DF
Data on daily units and sales (in $) of several marijuana products in Washington are available online. A researcher aims to test if the mean August sales per unit is associated to the product (Liquid
From the interaction plot below, do you think that factor A has an impact on response? Factor B? Do you think there is an interaction effect? Y 60 50 40 30- Low Factor A High Factor B No Yes
A teacher wants to check if there was a linear association between the final grade and the number of absences during the semester. Treating his class of 27 students as a random sample, Minitab
Download the file “Sustainability__2010-2013_Baltimore”, which has Baltimore data. Is dirtyst12 (rate of dirty streets and alleys Reports per 1000 residents) a good predictor of voted12 (% of
Download “Chicago_Public_Schools_ -_Progress_Report_Cards__2011- 2012_,” Chicago open data. We will assess the relationship between rate of misconduct per 100 students (response) and teachers’
Download the file “Census_Data_Selected_socioeconomic_indicators_ in_Chicago_2008_2012” with data from 77 communities in Chicago. Using statistical software, we will assess if percent of Housing
A simple linear regression model is constructed to see how well average American College Testing (ACT) scores in Chicago help predict college enrollment rate. Below, the residuals of the model are
A multinational corporation completed an analysis to model weekly sales, in dollars, using average production work hours per week. To present their work to pundits in Germany, they must convert the
The table below summarizes suicide rates for Asian men and women in New York City from 2007 until 2014. With the assistance of statistical software, test if gender predicts suicide rate. Use α =
While revising a report you received from an analyst, you come across a residual versus fit plot. It shows that all residuals were negative. How is this indicative of an issue?
Is there an association between starting post-college salary and hours a week playing video games? The table below summarizes the results from a sample of 100 randomly surveyed participants.
Download the file “Sanitation_2010 Baltimore,” which has 2010 Baltimore data for rate of dirty streets and alleys (dirtyst10) and rate of clogged drain reports per 1000 residents (drains10). Is
Show that the F statistic in Figure 13.12 is equal to the t statistic calculated from the data, squared. Regression Analysis: Median home value versus Median household income Analysis of
A new model of home selling price has been developed by a realty company. One way to assess if the coefficient estimates have been properly recorded is to construct a simple regression model of the
A company is aware that the mean cost of repairs on production machines is at least $625 a week. After a program to train employees on using the machines more effectively, the next 25 weeks are
In an attempt to increase daily sales of their coffee, Company C just implemented a large marketing campaign. A manager believes the marketing campaign was a failure. To test this, she decides to
With some given data, if you perform a two-sided test, you do not reject the null. But if you choose a one-sided test you do. How do you explain this?
Determine the appropriate mathematical symbol that corresponds to each statement: =, ≥, ≤,≠, >, or <.a) Mean SAT score of high school students is 625.b) The proportion of batteries
In what follows, write the expression for H0 according to the given H1.a) H1 ∶ μ > 103.2 ,b) H1 ∶ μ < 547 ,c) H1 ∶ μ ≠ 706.44 ,d) H1 ∶ π ≠ 0.75 ,e)
State what is wrong in each combination of null and alternative hypotheses:a) H0 ∶ μ = 17;H1∶ μ ≥ 17.b) H0 ∶ μ ≤ 29;H1∶ μ > 35.c) H0 ∶ π > 0.60;H1∶ π ≤ 0.60.d) H0 ∶ μ
Suppose a researcher sets α = 0.01. Interpret the meaning of this value of α.
Suppose β = 0.20. Interpret the meaning of this value of β.
In the following, find the power of the test and the probability of not rejecting the null when the null is true.a) α = 0.01, β = 0.10.b) α = 0.05, β = 0.20.c) α = 0.10, β = 0.05.d) α = 0.01,
Determine in the following whether type I, type II, or no error occursa) H0 ∶ μ ≤ 12 is not rejected. True population mean is 15.b) H0 ∶ μ ≥ 27 is rejected. True population mean is 35.c) H0
A firm was testing whether a new gadget design allowed an increase in its battery life. Specifically, if μ is the expected battery life in hours when the gadget is new, H0 ∶ μ ≤ 10.7 and
Definea) What is a pivotal quantity?b) What is a decision rule?
For a study, H0 ∶ μ = 50 and H1 ∶ μ ≠ 50. A two-sided confidence interval at confidence level 1 − α was found to be (35.7, 52.3). Do you think that conducting the hypothesis testing at the
For a study, H0 ∶ μ = 175 and H1 ∶ μ ≠ 175. A two-sided confidence interval at confidence level 1 − α was found to be (113.57, 126.83). Do you think the p-value will be smaller
A computer company wishes to install a fan that cools the equipment so that the temperature of the mother-board does not exceed a 115°F. A company inspector wishes to test the design of the computer
A firm is considering to use a new machine to reduce the current production time of 5.25 minutes for a product. Since they can try out the machine before purchase, they will take a random sample of
For over 25 years, Fishy company has been selling canned sardines, mainly with a net (mean) weight of 425 g. To your surprise, management has not tested the actual mean weight of cans in the last
Assuming a Z test statistic will be used, sketch the rejection region under the test statistic:a) H0 ∶ μ = 250;H1 ∶ μ ≠ 250; α = 0.05.b) H0 ∶ μ ≤ 181;H1 ∶ μ > 181;
Determine whether H0 should be rejecteda) p-Value = 0.32, α = 0.01.b) p-Value = 0.11, α = 0.05.c) p-Value = 0.99, α = 0.10.d) p-Value = 0.001, α = 0.05.e) p-Value = 0, α = 0.01.f) p-Value =
Say thatH0∶ μ ≥ 25.5H1∶ μ < 25.5If n = 50, σ = 5, and α = 0.01, and X̅ is normally distributed, compute the p-value and state if you reject the null or not whena) x̅ = 26.b) x̅ =
Suppose thatH0 ∶ μ ≤ 173.8H1 ∶ μ > 173.8If n = 42, σ = 21, and α = 0.05, and X̅ is normally distributed, compute the p-value and state if you reject the null or not whena) x̅ =
If a researcher by mistake wroteH0 ∶ μ > 25.5H1 ∶ μ ≤ 25.5Under this erroneous statement, what are the consequences for the rest of the hypothesis testing procedure?
A company is attempting to determine if the content of chemical X in their product is below a certain threshold. Specifically,H0 ∶ μ ≥ 30 mgH1 ∶ μ < 30 mgA random sample was taken
If H0 ∶ μ ≤ 40.5 and H1 ∶ μ > 40.5 , which of the following is an equivalent statement?a) H0 ∶ μ < 40.5; H1 ∶ μ ≥ 40.5.b) H0 ∶ μ = 40.5; H1 ∶ μ ≠ 40.5.c) H0 ∶ μ ≥
If H0 ∶ μ ≥ 73; H1 ∶ μ < 73, which of the following is an equivalent statement?a) H0 ∶ μ = 73; H1 ∶ μ < 73.b) H0 ∶ μ ≤ 73; H1 ∶ μ > 73.c) H0 ∶ μ = 73; H1 ∶ μ ≠
An engineer was proud to have installed a new solar system at his house. The system was economically feasible because the generated surplus power was sold to the power company. To the engineer’s
February 2018 daily page views for the Boston Archives website are available (“digitalrecords-pageviews-2018-02”).a) Find the mean and standard deviation of daily pageviews for February from the
A one-sided 90% confidence interval for the mean monthly cost of supplies for a printing service shop gave an upper bound of $714.a) Interpret the result of this confidence interval.b) Would the
A one-sided 99% confidence interval for the mean number of visits to a theme park in July gave a lower bound of 11 321.44.a) Interpret the result of this confidence interval.b) Would the equivalent
If H0 ∶ μ ≤ 11.4 but μ is in fact 13, σ = 4, n = 60, α = 0.05, and the value of X̅ to reject the null is 12.25, determine what is the power of the test.
Say thatH0 ∶ μ ≥ 25.5H1 ∶ μ < 25.5If n = 50, α = 0.01, and the population is normally distributed, use statistical software to compute the p-value and state if you reject the null or not
Suppose thatH0 ∶ μ ≤ 173.8H1 ∶ μ > 173.8If n = 42, α = 0.05, and the population is normally distributed, use statistical software to compute the p-value and state if you reject the null
Say thatH0 ∶ μ = 33.7H1 ∶ μ ≠ 33.7If n = 30, α = 0.05, and the population is normally distributed, compute the p-value and state if you reject the null or not whena) x̅ = 34, s =
A company claims that its food snacks contain an average of 25 g of sugar per serving. A researcher takes a random sample of 25 snack servings and finds an average of 32 g of sugar and a standard
Recently, a friend of yours who works at the local pizzeria stated that she is skeptical of the manager’s claim that they will deliver pizza in 30 minutes or less, anywhere in the local
After evaluating customer satisfaction survey data, a computer company finds that one of the main complaints of customers was how long it took to repair computers. They make some changes with the
According to public health officials, the 2007 US mortality rate of breast cancer was 22.9 per 100 000 women. Use Chicago data found in
Interpret the confidence interval in Figure 10.13. Does it support the conclusion reached with the hypothesis test? One-Sample T Test of μ = 500.71 vs > 500.71 Mean StDev SE Mean 99% Lower 15.9 N 23
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