Essential Mathematics And Statistics For Science 2nd Edition Graham Currell, Dr. Antony Dowman - Solutions

9.50 One way to evaluate the effectiveness of a teaching assistant is to examine the scores achieved by his or her students on an examination at the end of the course. Obviously, the mean score is of interest. However, the variance also contains useful information—some teachers have a style that
9.49 Plastic sheets produced by a machine are periodically monitored for possible fluctuations in thickness. If the true variance in thicknesses exceeds 1.65 square millimeters, there is cause for concern about product quality.Thickness measurements for a random sample of 10 sheets produced in a
9.44 Of a random sample of 199 auditors, 104 indicated some measure of agreement with this statement: Cash flow is an important indication of profitability.a. Test, at the 10% significance level against a two-sided alternative, the null hypothesis that one-half of the members of this population
9.43 In a random sample of 1,099 adults in a certain country, 21.3% of the sample members indicated some measure of disagreement with this statement: Globalization is more than an economic trade system—instead it includes institutions and culture.a. Test, at the 1% level, the null hypothesis that
9.33 Of a random sample of 214 auditors, 125 indicated some measure of agreement that cash flow is an important indication of profitability. Test at the 5%significance level against a two-sided alternative the null hypothesis that one-half of the members of this population would agree with the
9.32 In a random sample of 160 business school students, 72 sample members indicated some measure of agreement with this statement: Scores on a standardized entrance exam are less important for a student’s chance to succeed academically than is the student’s high school GPA.Test the null
9.31 In a random sample of 468 export managers in the United Kingdom, 90 members indicated some measure of disagreement with this statement: Globalization is more than an economic trade system—instead it includes institutions and culture. Test at the 5% level the hypothesis that at least 25% of
9.30 In a random sample of 472 owners of small businesses that had gone into bankruptcy, 352 reported conducting no marketing studies prior to opening the business. Test the hypothesis that at most 70% of all members of this population conducted no marketing studies before opening their businesses.
9.28 A random sample of women is obtained, and each person in the sample is asked if she would purchase a new shoe model. The new shoe model would be successful in meeting corporate profit objective if more than 25% of the women in the population would purchase this shoe model. The following
9.27 In contract negotiations a company claims that a new incentive scheme has resulted in average weekly earnings of at least $400 for all customer service workers.A union representative takes a random sample of 15 workers and finds that their weekly earnings have an average of $381.35 and a
9.24 A process that produces bottles of shampoo, when operating correctly, produces bottles whose contents weigh, on average, 20 ounces. A random sample of nine bottles from a single production run yielded the following content weights (in ounces):21.4 19.7 19.7 20.6 20.8 20.1 19.7 20.3 20.9
9.23 A company selling licenses for new e-commerce computer software advertises that firms using this software obtain, on average during the first year, a yield of 10% on their initial investments. A random sample of 10 of these franchises produced the following yields for the first year of
9.21 The accounts of a corporation show that, on average, accounts payable are $125.32. An auditor checked a random sample of 16 of these accounts. The sample mean was $131.78 and the sample standard deviation was $25.41. Assume that the population distribution is normal. Test at the 5%
9.19 A random sample of 171 employees was asked to rate, on a scale from 1 (not important) to 5 (extremely important), health benefits as a job characteristic. The sample mean rating was 2.07, and the sample standard deviation was 0.80. Test at the 10% significance level the null hypothesis that
9.13 A pharmaceutical manufacturer is concerned that the impurity concentration in pills should not exceed 3%. It is known that from a particular production run impurity concentrations follow a normal distribution with a standard deviation of 0.5%. A random sample of 81 pills from a production run
receives a shipment of batteries from Grenland Energy, a battery manufacturer in Skien, Norway, and tests a random sample of nine before agreeing to take it. Kongsberg is concerned that the true mean lifetime for all batteries in the shipment should be at least 50 hours. From past experience it is
9.12 Kongsberg Maritime, a Norwegian technology enterprise,
9.11 A manufacturer of cereals claims that the contents of boxes sold weigh on average at least 20 ounces. The distribution of weight is known to be normal, with a standard deviation of 0.5 ounce. A random sample of 25 boxes yielded a sample mean weight of 19.96 ounces.Test at the 10% significance
9.9 A random sample is obtained from a population with a variance of s2 = 400, and the sample mean is computed to be xc = 70. Consider the null hypothesis H0 : m = 80 versus the alternative hypothesis H1 : m 6 80. Compute the p-value for the following options.a. Sample size n = 25b. Sample size n =
9.8 A random sample of n = 25 is obtained from a population with variance s2, and the sample mean is computed.Test the null hypothesis H0 : m = 120 versus the alternative hypothesis H1 : m 7 120 with a = 0.10.Compute the critical value xc and state your decision rule for the following options.a.
9.6 Here we have the complement of Exercise 9.5. The 2000 presidential election in the United States was very close, and the decision came down to the results of the presidential voting in the state of Florida. The election was finally decided in favor of George W.Bush over Al Gore by a U.S.
9.5 The 2000 presidential election in the United States was very close, and the decision came down to the results of the presidential voting in the state of Florida.The election was finally decided in favor of George W. Bush over Al Gore by a U.S. Supreme Court decision that stated that it was not
9.4 Many people in Europe object to purchasing genetically modified food that is produced by farmers in the United States. The U.S. farmers argue that there is no scientific evidence to conclude that these products are not healthy. The Europeans argue that there still might be a problem with the
9.3 John Stull, senior vice president of manufacturing, is seeking strong evidence to support his hope that new operating procedures have reduced the percentage of underfilled cereal packages from the Ames production line. State his null and alternative hypotheses and indicate the results that
9.2 The board of a national central bank is meeting to decide if it should reduce interest rates in order to prevent deflation. State the null and alternative hypotheses regarding deflation that the board would formulate to guide its decision.
9.1 Mary Arnold wants to use the results of a random sample market survey to seek strong evidence that her brand of breakfast cereal has more than 20% of the total market. Formulate the null and alternative hypotheses, using P as the population proportion.
9.6 Tests of the Variance of a Normal Distribution
9.5 Assessing the Power of a Test Tests of the Mean of a Normal Distribution: Population Variance Known Power of Population Proportion Tests (Large Samples)
9.4 Tests of the Population Proportion (Large Samples)
9.3 Tests of the Mean of a Normal Distribution:Population Variance Unknown
9.2 Tests of the Mean of a Normal Distribution:Population Variance Known p-Value Two-Sided Alternative Hypothesis
9.1 Concepts of Hypothesis Testing
10.7 You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean defined as m1 and process 2 has a mean defined as m2.The null and alternative hypotheses are as follows:H0 : m1 - m2 … 0 H1 : m1 - m2 7 0 The
10.6 You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean defined as m1 and process 2 has a mean defined as m2.The null and alternative hypotheses are as follows:H0 : m1 - m2 = 0 H1 : m1 - m2 7 0 Use a
10.2 You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean defined as m1 and process 2 has a mean defined as m2. The null and alternative hypotheses are as follows:H0 : m1 - m2 Ú 0 H1 : m1 - m2 6 0 Using
11.9 Graphical Analysis
11.8 Beta Measure of Financial Risk
11.7 Correlation Analysis Hypothesis Test for Correlation
11.6 Prediction
11.5 Statistical Inference: Hypothesis Tests and Confidence Intervals Hypothesis Test for Population Slope Coefficient Using the F Distribution
11.4 The Explanatory Power of a Linear Regression Equation Coefficient of Determination, R2
11.3 Least Squares Coefficient Estimators Computer Computation of Regression Coefficients
11.2 Linear Regression Model
11.1 Overview of Linear Models
10.58 We will now understand the effects of another home condition: does the student have books at home to help with their school work? Using a random sample of 500 observations from the PISA database, to be found in the data file PISA Sample, analyze the difference in means of the mathematics and
10.57 Let us now investigate the effects of another home condition: does the student have access to the Internet at home? Using a random sample of 500 observations from the PISA database, to be found in the data file PISA Sample, analyze the difference in means of the mathematics and reading scores
10.56 Let us now investigate another home condition:can the student use educational software at home?Using a random sample of 500 observations from the PISA database, to be found in the data file PISA Sample, analyze the difference in means of the mathematics and reading scores between students who
10.55 Let us look at another home condition in this exercise:does the student have a computer for school work at home? Using a random sample of 500 observations from the PISA database, to be found in the data file PISA Sample, analyze the difference in means of the mathematics and reading scores of
10.54 In this exercise, let us look at a third home condition that might affect the reading and mathematics scores of 15-year-old students: does the student have a quiet place to study at home? Using a random sample of 500 observations from the PISA database, to be found in the data file PISA
10.53 In this exercise, we will be looking at another home condition that might affect the mathematics and readings scores of 15-year-old students: does the student have a room of their own at home? Using a random sample of 500 observations from the PISA database, to be found in the data file PISA
10.52 Another one of equity’s dimensions in the PISA studies is home conditions/facilities available to the student is also a factor. Does the education system succeed in adequately compensating for differences in students’ home situations? In this exercise, we will be looking at one of these
10.51 Equity is a major theme in the PISA studies of the mathematics and reading performance scores of 15-year-olds around the world. Equity has several dimensions, one of which is gender equity. Using a random sample of 500 observations from the PISA database, to be found in the data file PISA
10.48 Mortgage banks in a European country are very competitive, with institutions competing over market shares. As a local branch manager of Bank H, you are competing with the local branches of Bank S and Bank N. The data file Mortgage Banks contains the year-on-year growth rates of issued
10.46 We would like to investigate if positive and negative affect measure really different concepts(beyond the direction of these variables being opposite) in the United Nations’ World Happiness Report. To do so, we first reverse the negative affect score of each nation, by calculating
10.45 Most retail outlets like H&M, Zara, and Forever21 have an end-of-season sale in December every year.Suppose the manager of a retail chain in Arezzo, Italy, wants to know the sales for two outlets and determine the difference in sales between them. The sales report showed that outlet 1 located
10.44 The COVID-19 pandemic has significantly affected the real estate market in a country where there was a large decline in demand and nationwide home prices dropped to their lowest. To study the impact of the pandemic, a real estate company randomly selected 15 residential units’ prices (in $
10.43 Let us analyze if differences exist in the 2020 scores for SocialSupport, FreedomToMakeLifeChoices, and PerceptionsOfCorruption between African nations (Sub-Saharan Africa and North Africa together) and American nations (Latin America and Caribbean and North America together). Using the data
10.42 We will now investigate if differences exist in the 2020 scores for LadderChange, PosAffectChange, and NegAffectChange between African nations and American nations (taking the northern and southern regions together for both continents). Using the data file Happiness Report Data, prepare a
10.41 Independent random samples of employees in administration and support services were taken from an IT company to determine employee satisfaction levels.Of 36 administrative employees, 30 were satisfied, as were 42 of the 58 support service employees. Find and interpret the p-value of a test of
10.39 A random sample of online gamers was drawn from a gaming website that focused on skill development. Of a sample of 83 gamers who played multiplayer games, 64 had participated in BlizzCon, an annual gaming convention. Of an independent random sample of 95 gamers who played single-player games,
10.38 Aimed at finding monthly tips earned by the waiter and waitress in a restaurant, a random sample of 11 waiters at a restaurant showed that the mean monthly tips earned by them was $67.058, and the sample standard deviation was $12.50. An independent random sample of 9 waitresses in the same
10.37 Suppose Universiti Kuala Lumpur, Malaysia, offers business communication as an elective module. Of a random sample of 154 accounting students, 62 have taken the module. This same elective was taken by 44 students from an independent random sample of 137 finance majors.a. Test, at the 5%
10.35 A survey was conducted to determine the difference between the annual salaries of employees with and without a college degree. For a sample of 115 employees with a college degree, the mean salary per year was£45,248, and the sample standard deviation was £10,974.For a sample of 102
10.34 In this exercise, we will investigate if differences exist in the 2020 scores of SocialSupport, FreedomToMakeLifeChoices, and PerceptionsOfCorruption between European and Asian nations. Using the data file Happiness Report Data, analyze the difference in means in these three variables between
10.33 The World Happiness Report is an annual UN Sustainable Development Solutions Network publication. The first of this was published in 2011, in line with the Bhutanese Resolution passed by the UN General Assembly in June 2011 that invited national governments to “give more importance to
10.32 A study was conducted to determine the weight (in lbs)gained by babies after consuming two different brands of baby food (A and B) for three months. For a random sample of 10 babies who consumed brand A, the mean weight gained was 2.05 lbs, and the sample standard deviation was 0.28 lbs. For
10.30 Equities and bonds are two of the most traded asset classes. A financial analysist is interested to know the annual return rate performance between the equities and bonds. She randomly samples the annual return rate of equities and bonds. For a sample of 73 bonds, she found the mean rate was
10.29 In a study on the exercise habits of two groups of nonbinary individuals, A and B, a random sample of 36 people from group A indicated an average of 10.25 hours weekly exercise with a standard deviation of 2.25 hours.While a random sample of 42 people from group B indicated an average of 9.5
10.28 Researchers test the null hypothesis that the proportion of three-year-old children receiving their initial formal education in an urban location is the same as the proportion of those in a rural location. Based on sample data, the null hypothesis is rejected at the 10% significance level.
10.21 Of a random sample of 1,000 people in Denmark, 500 had a positive attitude toward TV salespeople. Of an independent random sample of 1,600 people in France, 730 had a positive attitude toward TV salespeople.Test, at the 10% level, the null hypothesis that the population proportions are equal,
10.14 Test the hypotheses H0 : Px - Py = 0 H1 : Px - Py 6 0 using the following statistics from random samples.a. pn x = 0.42, nx = 500;pn y = 0.50, ny = 600b. pn x = 0.60, nx = 500;pn y = 0.64, ny = 600c. pn x = 0.42, nx = 500;pn y = 0.49, ny = 600d. pn x = 0.25, nx = 500;pn y = 0.34, ny = 600e.
10.7 You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean defined as m1 and process 2 has a mean defined as m2.The null and alternative hypotheses are as follows:H0 : m1 - m2 … 0 H1 : m1 - m2 7 0 The
10.6 You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean defined as m1 and process 2 has a mean defined as m2.The null and alternative hypotheses are as follows:H0 : m1 - m2 = 0 H1 : m1 - m2 7 0 Use a
10.2 You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean defined as m1 and process 2 has a mean defined as m2. The null and alternative hypotheses are as follows:H0 : m1 - m2 Ú 0 H1 : m1 - m2 6 0 Using
10.5 Some Comments on Hypothesis Testing
10.4 Tests of the Equality of the Variances Between Two Normally Distributed Populations
10.3 Tests of the Difference Between Two Population Proportions(Large Samples)
10.2 Tests of the Difference Between Two Normal Population Means:Independent Samples Two Means, Independent Samples, Known Population Variances Two Means, Independent Samples, Unknown Population Variances Assumed to Be Equal Two Means, Independent Samples, Unknown Population Variances Not Assumed
10.1 Tests of the Difference Between Two Normal Population Means:Dependent Samples Two Means, Matched Pairs
9.73 The 2021 World Happiness Report provides the change in scores in 2020 compared to the average relevant scores from 2017 to 2019 for nations in ten regions across the world. Using the data file Happiness Report Data, create appropriate subsamples.Perform an analysis of the variables
9.71 A police officer is analyzing the crime index of a town in a region. He claims that the town has an average crime index of 45.25 with the population standard deviation being no more than 10. A random sample of 14 towns’ crime index provides the followings measures a8 i=1 xi = 560 and a 8i=1
9.70 When operating normally, a manufacturing process produces sheets of paper for which the mean weight of the active ingredient is 5 grams, and the standard deviation is 0.025 gram. For a random sample of 12 sheets the following weights of active ingredient (in grams) were found:4.97 5.00 4.98
9.68 You have accepted a job in Taiwan and want optimize your commuting costs and rental costs. You are in the process of finalizing an apartment.You are informed that a house in Taiwan is considered overpriced if it is sold at a price higher than 3,500 USD/m2. Use a classical hypothesis test to
9.67 As per the World Happiness Report, the worldwide average happiness score for 2020 is 5.53.Since the first report in 2012, Western European countries have scored above the overall average, unlike the nations of Sub-Saharan Africa, which have scored below the average. Using the data file
9.66 The World Happiness Report is an annual UN Sustainable Development Solutions Network publication. The first of this was published in 2011, in line with the Bhutanese Resolution passed by the UN General Assembly in June 2011 that invited national governments to “give more importance to
9.63 Of a random sample of 220 parcels, 50 parcels have been delivered after the estimated delivery time. Find the lowest level of significance for testing the null hypothesis that at most 25% of all parcels have been delivered after the estimated delivery time.
9.62 From a random sample of 80 employees, 30 employees are enrolled in an external training program. Test at the 5% level the null hypothesis that at most 20%of the employees are enrolled in the external training program.
9.61 In a random sample of 110 applicants for an editorial job, 58 applicants fulfilled the job requirements.Find the lowest level of significance for testing the null hypothesis that the half of the applicants are fully qualified for the job against the alternative that a majority are fully
9.60 A survey was conducted to determine the most popular shopping websites by selecting a random sample of 200 online shoppers from a population of 800 shoppers.The people taking the survey were asked about the variety of products, clarity and appropriateness of product details, product reviews,
9.57 A financial analyst is investigating the return rate of mutual funds. He claims that mutual funds have a return rate of 0.10 per annum with a population standard deviation of no more than 0.13. A random sample of annual return rates for eight mutual funds are recorded, a 8i=1 xi = 1.2 and a
9.55 A random sample of 10 savings accounts was selected from DirectMe Bank in Brussels, Belgium. The daily minimum transaction amount (in €) for each account was recorded below:1,400 690 1,950 740 920 2,410 695 1,635 750 1,520 Assume that the population distribution is normal.a. Find the sample
9.53 Based on your understanding of each of the following pairs of terms, provide an example to differentiate them.a. Null and alternative hypothesesb. Simple and composite hypothesesc. One-sided and two-sided alternativesd. Type I and Type II errorse. Significance level and (1 – power)9.54
9.51 A company produces electric devices operated by a thermostatic control. The standard deviation of the temperature at which these controls actually operate should not exceed 2.0°F. For a random sample of 20 of these controls, the sample standard deviation of operating temperatures was 2.36°F.
9.49 Plastic sheets produced by a machine are periodically monitored for possible fluctuations in thickness. If the true variance in thicknesses exceeds 1.65 square millimeters, there is cause for concern about product quality.Thickness measurements for a random sample of 10 sheets produced in a
9.47 At the 5% significance level, test the hypotheses H0 : s2 … 20 H1 : s2 7 20 using the following results from the following random samples.a. s2 = 32; n = 15c. s = 5; n = 30b. s2 = 48; n = 28d. s = 10; n = 19 Application Exercises
9.38 Consider Example 9.6 with the null hypothesis H0 : P = P0 = 0.50 and the alternative hypothesis H0 : P ? 0.50 The decision rule is pn x - 0.50 10.5011 - 0.502>600 6 -1.96 or pn x - 0.50 10.5011 - 0.502>600 7 1.96 with a sample size of n = 600. What is the probability of Type II error if the
9.37 Consider a problem with the hypothesis test H0 : m = 5 H1 : m 7 5 and the following decision rule:reject H0 if x - 5 0.1>116 7 1.645 or x 7 5 + 1.64510.1>1162 = 5.041 Compute the probability of Type II error and the power for the following true population means.a. m = 5.10b. m = 5.03c. m =
9.29 A company is attempting to determine if it should retain a previously popular shoe model. A random sample of women is obtained, and each person in the sample is asked if she would purchase this existing shoe model. To determine if the old shoe model should be retained, the following hypothesis
9.28 A random sample of women is obtained, and each person in the sample is asked if she would purchase a new shoe model. The new shoe model would be successful in meeting corporate profit objective if more than 25% of the women in the population would purchase this shoe model. The following
9.25 A statistics instructor is interested in the ability of students to assess the difficulty of a test they have taken.This test was taken by a large group of students, and the average score was 80.3. A random sample of eight students was asked to predict this average score. Their predictions

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Essential Mathematics And Statistics For Science 2nd Edition Graham Currell, Dr. Antony Dowman - Solutions

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