Questions and Answers of Principles Of Managerial Statistics

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
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

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