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

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
9.22 On the basis of a random sample the null hypothesis H0 : m = m0 is tested against the alternative H1 : m 7 m0 and the null hypothesis is not rejected at the 5% significance level.a. Does this necessarily imply that m0 is contained in the 95% confidence interval for m?b. Does this necessarily
9.14 Test the hypotheses H0 : m … 100 H1 : m 7 100 using a random sample of n = 36, a probability of Type I error equal to 0.05, and the following sample statistics.a. x = 108; s = 20b. x = 104; s = 10c. x = 96; s = 10d. x = 95; s = 8 9.15 Test the hypotheses H0 : m … 100 H1 : m 7 100 using a
9.10 A random sample of n = 25 is obtained from a population with variance s2, and the sample mean is computed to be x = 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. The population variance is s2 =
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.
9.7 A random sample is obtained from a population with variance s2 = 625, and the sample mean is computed.Test the null hypothesis H0 : m = 100 versus the alternative hypothesis H1 : m 7 100 with a = 0.05. 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.
9.3 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
9.6 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
8.31 Brämhults Juice, based in Sweden, produces chilled fruit and vegetable juices. A manager at Brämhults is considering purchasing a new machine to bottle 16-fluid-ounce (473-milliliter) bottles of 100% pure carrot juice and wants an estimate of the difference in the mean filling weights
8.30 A tuition center employs two statistics professors. The head of the tuition center wants to know if there is a significant difference in the average final exam scores between the students taught by the two professors.Answer this question with a 90% confidence interval using the following data
8.28 To increase the fertility of his crops, a maize farmer adds two types of fertilizers, A and B, to two different areas of his farmland. He selects a random sample of 11 ears of maize planted using fertilizer A and finds that they have an average length of 6.5 inches with a sample standard
8.27 Independent random samples from two normally distributed populations give the following results:nx = 8 x = 77 sx = 6 ny = 13 y = 82 sy = 5a. If we assume that the unknown population variances are equal, find the 90% confidence interval for the difference of population means.b. If we do not
8.26 Independent random samples from two normally distributed populations give the following results:nx = 22 x = 2500 sx = 250 ny = 20 y = 2100 sy = 100 If we do not assume that the unknown population variances are equal, what is the 99% confidence interval for the difference between the population
8.25 Independent random samples from two normally distributed populations give the following results:nx = 10 x = 250 sx = 14 ny = 17 y = 165 sy = 23 Assume that the unknown population variances are equal and find a 95% confidence interval for the difference between population means.
8.19 Calculate the 95% confidence interval for the difference in population proportions for each of the following:a. nx = 260 pn x = 0.35 ny = 240 pn y = 0.30b. nx = 145 pn x = 0.20 ny = 120 pn y = 0.25 Application Exercises
8.18 Calculate the margin of error for each of the following:a. nx = 300 pn x = 0.62 ny = 350 pn y = 0.72b. nx = 100 pn x = 0.44 ny = 120 pn y = 0.55
8.11 Determine the margin of error for a 95% confidence interval for the difference between population means for each of the following (assume equal population variances):a. nx = 100 s2x= 36 x = 300 ny = 64 s2y= 49 y = 320b. nx = 25 s2x = 36 x = 300 ny = 16 s2y = 49 y = 320c. The sample sizes in
8.10 Assuming unequal population variances, determine the number of degrees of freedom for each of the following:a. nx = 16 s2x= 5 ny = 4 s2y= 36b. nx = 9 s2x= 30 ny = 16 s2y= 4
8.8 Assuming equal population variances, determine the number of degrees of freedom for each of the following:a. nx = 16 s2x= 30 ny = 9 s2y= 36b. nx = 12 s2x= 30 ny = 14 s2y= 36c. nx = 20 s2x= 16 ny = 8 s2y= 25 8.9 Assuming equal population variances, compute the pooled sample variance s2p for part
8.7 Independent random sampling from two normally distributed populations gives the following results:nx = 81; x = 140; s2x= 25 ny = 100; y = 120; s2y= 14 Find a 95% confidence interval estimate of the difference between the means of the two populations.
8.6 Independent random sampling from two normally distributed populations gives the following results:nx = 87; x = 115; sx = 25 ny = 88; y = 109; sy = 15 Find a 99% confidence interval estimate of the difference in the means of the two populations.
8.5 A random sample of six salespeople who attended a motivational course on sales techniques was monitored 3 months before and 3 months after the course.The table shows the values of sales (in thousands of euros) generated by these six salespeople in the two periods. Assume that the population
8.4 A random sample of 10 pairs of identical houses was chosen in a large Midwestern city, and a passive solar heating system was installed in one house from each pair. The total fuel bills (in dollars) for three winter months for these homes were then determined, as shown in the accompanying
8.3 An educational study was designed to investigate the effectiveness of a reading program of elementary age children. Each child was given a pretest and posttest.Higher posttest scores would indicate reading improvement.From a very large population, a random sample of scores for the pretest and
8.1 A dependent random sample from two normally distributed populations gives the following results:n = 11 d = 28.5 sd = 3.3a. Find the 98% confidence interval for the difference between the means of the two populations.b. Find the margin of error for a 98% confidence interval for the difference
8.3 Confidence Interval Estimation of the Difference Between Two Population Proportions (Large Samples)
8.2 Confidence Interval Estimation of the Difference Between Two Normal Population Means: Independent Samples Two Means, Independent Samples, and Known Population Variances Two Means, Independent Samples, and Unknown Population Variances Assumed to Be Equal Two Means, Independent Samples, and
8.1 Confidence Interval Estimation of the Difference Between Two Normal Population Means: Dependent Samples
7.94 Japan’s rainy season starts in July and continues through August. From a random sample of 40 days in 2021, the mean temperature was around 26.3°C with a standard deviation of 1.6°C. Compute the 90% confidence interval estimate of Japan’s mean temperature in July and August.7.95 Fifty
7.92 Consider the data in Exercise 7.90. It was reported in the local paper that almost two-thirds (from 57%to 63%) of the population prefers the online renewal process. What is the confidence level of this interval estimate?7.93 The county finance department in Exercise 7.90 also wants information
7.91 Consider the data in Exercise 7.90. Suppose that we computed for the population proportion who pay for vehicle registration by mail a confidence interval extending from 0.15 to 0.17. What is the confidence level of this interval?
7.89 The following data represent the scores obtained from a random sample of 20 people who attempted an IQ test having a maximum score of 100:85 92 54 46 98 70 63 56 95 40 57 98 81 47 72 40 68 41 70 94a. What is the reliability factor for a 90% confidence interval estimate of the mean IQ test
7.88 A restaurant conducted a survey to determine whether customers are satisfied with its food delivery service by clicking “Yes” or “No” on an online form shared with them. From a random sample of 440 responses, it found that 278 customers selected“Yes.”a. Find the standard error to
7.85 A teacher selected a random sample of 170 primary students from her school. They were asked what amount they received as daily pocket money. The sample mean response was €2.50, and the sample standard deviation was €1.85. Based on these results, the teacher determined a confidence interval
7.83 Students’ scores on the final statistics test from the previous semester at a university were taken for a random sample of 9 students and were recorded as follows:69 92 82 30 73 91 48 74 62a. Find the most efficient estimates of the population mean and variance.b. Estimate the proportion of
7.82 Suppose the manager of Croquettenbar Smaeck, a restaurant in Antwerp, Belgium, is estimating the queuing time of the customers until they receive their meals during peak hours. From a random sample of 18 customers, the average queuing time is 15 minutes with a standard deviation of 3.5
7.81 The following data represent the exchange rate of Malaysian ringgit (RMY) to Hong Kong dollar (HKD), retrieved from the Interbank Foreign Exchange Market in Kuala Lumpur, Malaysia, from September 10, 2021 to October 8, 2021.54.3511 54.3409 54.3687 54.2803 54.2483 54.2774 54.4619 54.4398
7.79 Students at a university in Ghent, Belgium, are expected to complete a group presentation in 20 minutes as one of the assessments to pass the business module. In a random sample of 18 presentations, the module leader finds a mean duration of 17 minutes with a standard deviation of 5 minutes.
7.78 Wosiwosi, a UK-based African food store, specializes in the distribution of wholesale and retail of African and Caribbean food. Suppose the manager wants to estimate the mean amount customers will spend on their next visit. An analyst studies customers’ expenditures per visit. From a random
7.73 Determine the sample size needed for each of the following situations.a. N = 5,000; pn = 0.5; 1.96spn = 0.10b. N = 5,000; pn = 0.5; 1.96spn = 0.05 Application Exercises
7.72 Determine the sample size needed for each of the following situations.a. N = 1,000; s = 450; 1.96sx = 50b. N = 3,000; s = 450; 1.96sx = 50c. N = 1,000,000; s = 450; 1.96sx = 50d. Compare and comment on your answers to parts a through c.
7.71 Determine the sample size needed for each of the following situations.a. N = 785; s = 24; 1.96sx = 5b. N = 785; s = 24; 1.96sx = 88c. N = 785; s = 24; 1.96sx = 190d. Compare and comment on your answers to parts a through c.
7.67 How large a sample is needed to estimate the population proportion for each of the following?a. ME = 0.05; a = 0.01b. ME = 0.05; a = 0.10c. Compare and comment on your answers to parts a and b.Application Exercises
7.66 How large a sample is needed to estimate the population proportion for each of the following?a. ME = 0.03; a = 0.05b. ME = 0.05; a = 0.05c. Compare and comment on your answers to parts a and b.
7.55 Take a random sample of 80 pages from this book and estimate the proportion of all pages that contain mathematical formulas.
7.54 Assume simple random sampling. Calculate the confidence interval for the population proportion, P, for each of the following.a. N = 1,675; n = 400; x = 120; 99% confidence levelb. N = 955; n = 100; x = 30; 95% confidence level Application Exercises
7.51 Assume simple random sampling. Calculate the variance of the sample mean, s2x, for each of the following.a. N = 1,300; n = 100; s = 15b. N = 1,500; n = 200; s2 = 91c. N = 3,000; n = 220; s2 = 150
7.50 A watch manufacturer in Switzerland uses sputtered titanium coating for some models it creates. A random sample of nine observations on the thickness of this coating is taken from a week’s output, and the recorded thicknesses (in millimeters) are as follows:19.5 21.4 18.7 20.3 21.7 19.1 19.5
7.42.7.44 Consider the following random sample from a normal population:11 17 8 7 9a. Find the 90% confidence interval for population variance.b. Find the 95% confidence interval for the population variance.Application Exercises
7.42 Find the lower confidence limit for the population variance for each of the following normal populations.a. n = 21; a = 0.05; s2 = 16b. n = 16; a = 0.05; s = 8c. n = 28; a = 0.01; s = 15 7.43 Find the upper confidence limit for parts a–c of Exercise
7.32 A small private university is planning to start a volunteer football program. A random sample of alumni is surveyed. It was found that 250 were in favor of this program, 75 were opposed, and 25 had no opinion.a. Estimate the percent of alumni in favor of this program.Let a = 0.05.b. Estimate
7.31 Calculate the confidence interval to estimate the population proportion for each of the following.a. 90% confidence level; n = 700; pn = 0.20b. 99% confidence level; n = 140; pn = 0.01c. a = 0.03; n = 345; pn = 0.90
7.30 Find the margin of error to estimate the population proportion for each of the following.a. n = 350; pn = 0.30; a = 0.01b. n = 275; pn = 0.45; a = 0.05c. n = 500; pn = 0.05; a = 0.10
7.29 Build Rental is a plant hire company in the United Kingdom that provides machinery, equipment, and tools for a limited period to construction contractors.It is interested in the amount of time its equipment are out of operation for repair work. State all assumptions and find a 90% confidence
7.27 Weight Medics, a clinic in the United Kingdom, offers a weight-loss program for its clients. A review of its records found the following amounts of weight loss, in pounds, for a random sample of 20 clients at the end of a 4-month program:24 19 5 12 16 10 18 15 8 17 11 6 14 8 19 22 13 20 11
7.26 There is concern about the speed of automobiles traveling over a particular stretch of highway. For a random sample of 28 automobiles, radar indicated the following speeds, in miles per hour:59 63 68 57 56 71 59 69 53 58 60 66 51 59 54 64 58 57 66 61 65 70 63 65 57 56 61 59 Assuming a normal
7.23 The Programme for International Student Assessment(PISA) is a global study conducted by the Organization for Economic Co-operation and Development(OECD). It measures mathematical performance as the mathematical literacy of 15-year-old students to formulate, employ, and interpret mathematics in
7.22 Calculate the width for each of the following.a. n = 6; s = 40; a = 0.05b. n = 22; s2 = 400; a = 0.01c. n = 25; s = 50; a = 0.10 Application Exercises
7.20 Find the LCL and UCL for each of the following.a. a = 0.05; n = 25; x = 560; s = 45b. a>2 = 0.05; n = 9; x = 160; s2 = 36c. 1 - a = 0.98; n = 22; x = 58; s = 15
7.17 Find the standard error to estimate the population mean for each of the following.a. n = 17; 95% confidence level; s = 16b. n = 25; 90% confidence level; s2 = 43 7.18 Calculate the margin of error to estimate the population mean for each of the following.a. 99% confidence level;x1 = 25; x2 =
7.12 Assume a normal distribution with known population variance. Calculate the LCL and UCL for each of the following.a. x = 255; n = 304; s = 30; a = 0.01b. x = 395; n = 105; s2 = 100; a = 0.05c. x = 510; n = 485; s = 50; a = 0.10 Application Exercises
7.11 Assume a normal distribution with known population variance. Calculate the width to estimate the population mean, m, for the following.a. 90% confidence level; n = 100; s2 = 169b. 95% confidence level; n = 120; s = 25
7.10 Assume a normal distribution with known population variance. Calculate the margin of error to estimate the population mean for the following.a. 99% confidence level; n = 81; s2 = 169b. 90% confidence level; n = 200; s = 120
7.9 Find the reliability factor, za 2, to estimate the mean, m, of a normally distributed population with known population variance for the following.a. a = 0.09b. a2 = 0.01
7.7 Suppose that x1 and x2 are random samples of observations from a population with mean m and variance s2. Consider the following three point estimators, X, Y, Z, of m:X =1 2x1 +1 2x2 Y =1 4x1 +3 4x2 Z =1 3x1 +2 3x2a. Show that all three estimators are unbiased.b. Which of the estimators is the
7.6 According to CleanTechnica website, Sweden’s full electric vehicles took a record high 24.1%share of new sales, with the Kia e-Niro being Sweden’s best-selling full electric vehicle. Suppose you are an employee at a Kia showroom in Sweden. You are asked by your manager to provide an
7.4 A random sample of 15 employees in a large manufacturing plant found the following figures for number of hours of overtime worked in the last month:24 16 17 18 21 17 16 19 19 24 15 19 18 21 24 Use unbiased estimation procedures to find point estimates for the following:a. The population meanb.
7.3 A random sample of 10 economists produced the following forecasts for percentage unemployment rate in the next year:4.4 4.2 3.7 3.9 4.4 3.9 3.7 4.0 4.1 4.0a. The population meanb. The population variancec. The variance of the sample meand. The population proportion of economists predicting
7.2 A random sample of 10 homes in a particular suburb had the following selling prices (in thousands of pounds):209 256 257 272 275 277 278 285 306 327a. Check for evidence of nonnormality.b. Find a point estimate of the population mean that is unbiased and efficient.c. Use an unbiased estimation
7.1 There is concern about the speed of automobiles traveling over a particular stretch of highway. For a random sample of 28 automobiles, radar indicated the following speeds, in miles per hour:58 63 68 57 56 72 58 69 53 55 61 66 51 59 54 64 58 57 66 61 65 70 63 65 57 56 61 59a. Check for evidence
7.8 Sample-Size Determination: Finite Populations Sample Sizes for Simple Random Sampling: Estimation of the Population Mean or Total Sample Sizes for Simple Random Sampling: Estimation of Population Proportion
7.7 Sample-Size Determination: Large Populations Mean of a Normally Distributed Population, Known Population Variance Population Proportion
7.6 Confidence Interval Estimation: Finite Populations Population Mean and Population Total Population Proportion
7.5 Confidence Interval Estimation for the Variance of a Normal Distribution
7.4 Confidence Interval Estimation for Population Proportion(Large Samples)
7.3 Confidence Interval Estimation for the Mean of a Normal Distribution:Population Variance Unknown Student’s t Distribution Intervals Based on the Student’s t Distribution
7.2 Confidence Interval Estimation for the Mean of a Normal Distribution:Population Variance Known Intervals Based on the Normal Distribution Reducing Margin of Error
7.1 Properties of Point Estimators Unbiased Most Efficient
6.76 Scores on a particular test, taken by a large group of students, follow a normal distribution with a variance of 2500. A random sample of 25 scores was taken to estimate the population’s mean score. Let the random variable x denote the sample mean. What is the probability that the interval
6.73 The length of the Atlantic salmon sold by a fishmonger has a normal distribution with a standard deviation of 2 inches. A random sample of 9 Atlantic salmons is selected from the fishmonger.a. The probability is 0.05 that the sample standard deviation of the lengths of the Atlantic salmon
6.72 It is found that out of a group of elders, 65% have high glucose levels. Suppose their glucose level is normally distributed with a mean of 13 mmol/L and a standard deviation of 1.5 mmol/L.a. For a random sample of 40 elders, what is the probability that less than 50% have high glucose
6.71 It has been found the retirement age of a community follows a normal distribution with a mean of 75 years and a standard deviation of 3 years. A random sample of 11 people from the community is taken.a. What is the probability that the sample mean retirement age taken is more than 77 years?b.
6.70 Refer to the chapter appendix in order to derive the mean of the sampling distribution of the sample variances for a sample of n observations from a population of N members when the population variance is s2. By appropriately modifying the argument regarding variances in the chapter appendix,
6.69 The gross area values of the lands sold by a property agency are known to be normally distributed with a mean of 999 acres and a standard deviation of 250 acres.a. For a random sample of 8 lands, find the probability that the sample mean is more than 900 acres.b. For a random sample of 8
6.68 A bank web operation officer is monitoring online credit card transactions and determines that the transaction duration follows a normal distribution with a mean of 20 seconds and a standard deviation of 7 seconds.A random sample of 16 such transaction durations is taken.a. What is the
6.67 A flour manufacturer found that the weightage error of bags labeled 2 kilograms of flour follows a normal distribution with a mean of 10 grams and a standard deviation of 2 grams. A random sample of 5 bags of 2 kilograms flour each was taken.a. What is the probability that the sample mean
6.66 A study determines that the height of Taiwanese men aged 65 or more is normally distributed with an average of 163.8 centimeters and standard deviation of 6.2 centimeters. A random sample of 20 Taiwanese elderly men is taken.a. Find the probability that the sample mean height is higher than
6.65 Explain how the central limit theorem works on the sampling distribution of the sample means from a population that is normally distributed and one that is not normally distributed.
6.63 What is meant by the statement that the sample mean and the sample proportion have a sampling distribution?What other statistical examples can you provide?
6.52 It is believed that first-year salaries for newly qualified accountants follow a normal distribution with a standard deviation of $2,500. A random sample of 16 observations was taken.a. Find the probability that the sample standard deviation is more than $3,000.b. Find the probability that the
6.50 The athletic association of a school reports that the men’s 100-meter run follows a normal distribution with a variance of 1.58 seconds. A random sample of 23 records of the men’s 100-meter run are randomly selected. Find the probability that the sample variance exceeds 1.99 seconds.
6.49 A random sample of size n = 11 is obtained from a normally distributed population with a population mean of m = 27 and a variance of s2 = 16.a. What is the probability that the sample mean is greater than 30?b. What is the value of the sample variance such that 1%of the sample variances would
6.48 A random sample of size n = 16 is obtained from a normally distributed population with a population mean of m = 114 and a variance of s2 = 484.a. What is the probability that the sample mean is greater than 120?b. What is the value of the sample variance such that 10% of the sample variances

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

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