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probability statistics

Using And Interpreting Statistics 3rd Edition Eric W. Corty - Solutions

5. Reconsider the data in Problem 6 of Section 2.3, reproduced here:105 101 120 116 108 112 118 119 107 100 107 120 113 113 101 102 102 100 101 100 118 106 114 100 104 101 107 113 110 100 109 108 100 104 110 113 118 100 119 120(a) Determine the mean, median, and mode for these data.(b) Determine
4. Reconsider the data in Problem 5 of Section 2.3, reproduced here:148 167 171 177 175 165 134 177 168 142 126 166 130 122 157 138 163 129 143 145 141 162 147 141 164 137 149 146 132 157(a) Determine the mean and median for these data.(b) Determine the range, variance, and the standard deviation
3. Reconsider the data in Problem 4 of Section 2.3, reproduced below:25 30 26 26 25 16 21 22 21 27 15 24 19 20 24 16 30 28 24 23 15 15 21 28 18 15 21 27 26 28 17 19 24 26 27 17 27 19 22 27 16 25 16 30 18(a) Determine the mean and median for these data.(b) Determine the standard deviation for these
2. Use the values of the mean (¯X) and the standard deviation (S) found in Problem 1 to determine the number of data points that fall in the intervals (¯X − S, ¯X +S), (¯X − 2S, ¯X + 2S), and (¯X − 3S, ¯X + 3S). Assuming that the distribution of this data set is bell-shaped, use the
1. The data given below gives the viscosity of paper pulp measured over a period of 30 days:117.9 117.7 121.9 116.8 118.9 121.2 119.0 117.5 120.1 122.6 120.1 124.1 120.1 118.4 117.2 121.7 122.2 122.0 121.2 120.4 119.8 121.6 118.1 119.3 121.1 119.6 117.9 119.4 120.8 122.1(a) Determine the mean,
15. The following data give the consumption of electricity in kilowatt-hours during a given month in 30 rural households in Maine:260 290 280 240 250 230 310 305 264 286 262 241 209 226 278 206 217 247 268 207 226 247 250 260 264 233 213 265 206 225(a) Construct, using technology, a stem-and-leaf
14. Refer to the data in Problem 13 above. Construct a stem-and-leaf diagram for these data.
13. Compressive strengths were measured on 60 samples of a new metal that a car manufacturing company is considering for use in bumpers with better shock-absorbent properties. The data are shown below:59.7 58.3 59.0 61.5 58.7 63.8 68.2 65.6 63.5 62.4 59.4 63.2 64.5 60.0 60.5 61.5 68.5 66.6 61.3
12. The following data give the number of accidents per week in a manufacturing plant during a period of 25 weeks:0 4 1 2 3 4 2 1 0 3 4 0 2 1 3 2 4 2 0 5 3 5 0 1 4 50 2 Describing Data Graphically and Numerically(a) Construct a single-valued frequency distribution table for these data.(b) Construct
11. A manufacturer of a part is interested in finding the life span of the part. A random sample of 30 parts gave the following life spans (in months):23 25 30 32 36 42 28 24 21 43 46 48 39 30 34 35 24 21 16 54 25 34 37 23 24 28 26 19 27 37 Construct a relative frequency histogram and a cumulative
10. The following data give the number of parts that do not meet certain specifications in 50 consecutive batches manufactured in a given plant of a company:16 19 22 25 27 18 36 30 20 24 29 40 30 31 34 36 21 25 24 28 26 30 24 16 19 21 30 24 20 22 24 32 27 18 24 20 17 33 35 29 32 36 39 28 26 17 18
9. The following data give the number of patients treated per day during the month of August at an outpatient clinic in a small California town:20 30 25 35 32 46 40 38 44 41 37 35 40 41 43 38 37 35 32 40 23 26 27 29 21 23 28 33 39 20 29(a) Prepare a complete frequency distribution table for the
8. A manufacturer of men’s shirts is interested in finding the percentage of cotton in fabric used for shirts that are in greater demand. In order to achieve her goal, she took a random sample of 30 men who bought shirts from a targeted market. The 2.4 Graphical Description of Qualitative and
7. A manufacturing company is very training oriented. Every month the company sends some of its engineers for six-sigma training. The following data give the number of engineers who were sent for six-sigma training during the past 30 months:18 20 16 30 14 16 22 24 16 14 16 19 18 24 23 28 18 12 18
6. Construct a stem-and-leaf diagram for the data in Problem 6 of Section 2.3. Then, reconstruct the stem-and-leaf diagram you just made by dividing each stem into two stems and comment on which diagram is more informative.
5. Construct two stem-and-leaf diagrams for the data in Problem 4 of Section 2.3, using increments of 10 and 5, and comment on which diagram is more informative.
4. Use the data in Problem 6 of Section 2.3 to do the following:(a) Construct a frequency histogram for these data.(b) Construct a relative frequency histogram for these data.(c) Construct a frequency polygon for these data.(d) Construct an ogive curve for these data.
3. Prepare a line graph for the data in Problem 5 of Section 2.3 and state whether these data show any patterns. Read the data columnwise.
2. Prepare a pie chart and bar chart for the data in Problem 3 of Section 2.3 and comment on the cars the senior citizens like to drive.
1. Prepare a pie chart and bar chart for the data in Problem 2 of Section 2.3.
6. A temperature-sensing vacuum switch controls the vacuum that is applied to a vacuum motor operating a valve in the intake snorkel of the air cleaner. As the engine warms up, the temperature-sensing unit shuts off the vacuum applied to the motor, allowing the valve to close so that heated air
5. The following data give the number of graduate students admitted in all engineering programs of a prestigious university during the past 30 years (1976–2005).148 167 171 177 175 165 134 177 168 142 126 166 130 122 157 138 163 129 143 145 141 162 147 141 164 137 149 146 132 157 Prepare a
4. A manufacturing company of condenser retaining bolts for car engines implemented a quality control system. As part of this quality control system, a team of engineers decided to record the number of nonconforming bolts produced in each shift. The following data show the number of nonconforming
3. The following data give the responses of 36 senior citizens who were asked about the engine size of their car. The numbers 1, 2, 3, 4, and 5 represent the five categories 3.5, 3.2, 3.0, 2.2, and 1.8L, respectively.5 4 5 5 1 2 1 1 1 3 5 1 5 4 2 1 3 1 3 2 3 4 1 2 2 1 5 5 3 1 5 2 1 2 2 5(a) Prepare
2. An engineering school arranged a charity concert to raise funds for Iraq war veterans.The following data give the status of 40 randomly selected students who attended the concert. The numbers 1, 2, 3, and 4 represent the categories freshman, sophomore, junior, and senior, respectively.2 3 4 1 1
1. The following data give the results of a customer sample survey for product satisfaction conducted by a manufacturing company. The numbers 1, 2, 3, 4, and 5 represent the satisfaction levels: very satisfied, fairly satisfied, neutral, fairly unsatisfied, and very unsatisfied, respectively.1 1 3
6. A consumer protection agency conducts opinion polls to determine the quality(excellent, good, fair, bad) of products imported from an Asian country. Suppose that the agency conducted a poll in which 1000 randomly selected individuals were contacted by telephone.(a) What is the population of
5. Referring to Problem 4, classify the data in each case as nominal, ordinal, interval, or ratio.
4. Describe whether each of the following scenarios would result in qualitative or quantitative data:(a) Time needed to finish a project by a technician(b) Number of days of stay in a hospital by a patient after bypass surgery(c) Average number of cars passing through a toll booth each day(d) Types
3. A university professor is interested in knowing the average GPA of a graduating class. The professor decided to record the GPA of only those students who were 20 2 Describing Data Graphically and Numerically in his/her class during the last semester before graduation. Using this information(the
2. Describe the difference between descriptive statistics and inferential statistics.
1. Describe briefly the difference between a sample and a population. Give an example of a population and a sample.
and 8.93. (a) What is the impact of sample size on rejecting the null hypothesis? (b) On conclusions about the effectiveness of treatment? (c) On the size of the effect as determined by r 2? (d) On the confidence interval?
Compare your answers for Exercises
Dr. Brigham decided to replicate Dr. Goddard’s study (see Exercise 8.92) with a larger sample. She did exactly what Dr. Goddard did, but had 1,002 subjects (501 in the control group and 501 in the experimental group). The means for the two groups were exactly the same, 100 and 102, and both
Dr. Goddard developed a technique that he thought would increase IQ in adults. He obtained a random sample of 52 adult Americans and randomly assigned half of them to a control group and half to the experimental group. He did nothing to the control group, but he administered his IQ-increasing
Margery collected some data from two independent groups and analyzed them with an independent-samples t test. No assumptions were violated and she rejected the null hypothesis. Yet, when she calculated a confidence interval for the difference between population means, the confidence interval
Explain why the critical value of t, one-tailed, α = .05 is the same as the critical value of t, two-tailed, α = .10.
A consumer group is planning to do 2 two-sample t tests. In Test 1, they are going to put together a random sample of items at a jewelry store and compare the prices to a random sample of items at a bookstore, in order to see which store is more expensive. In Test 2, they are planning to compare a
Which result cannot be true for an independent-samples t test?a. A researcher has rejected the null hypothesis and found d =1.50.b. A researcher has failed to reject the null hypothesis and found d= 1.50.
A researcher completes an independent-samples t test and finds that the probability of two sample means being this far apart, if the null hypothesis is true, is less than .05. Which of the following is true?a. μ1 = μ2b. M1 ≠ μc. There probably is no difference between the two population
An addictions researcher measured tolerance to alcohol in first-year and fourth-year college students. She gave participants a standard dose of alcohol and then had them walk along a narrow line painted on the floor. The higher the percentage of the distance that they were on the line, the greater
A physician compared the cholesterol levels of a representative sample of Americans who ate an American diet vs. a representative sample of those who followed a Mediterranean diet. Below are the means, standard deviations, and sample sizes for both samples.Though in some studies a Mediterranean
A nutritionist compared the effectiveness of an online diet program to that of an in-person diet program. After three months, she compared the number of pounds of weight lost. The control group(in-person) lost a mean of 18.00 pounds (s = 14.50, n = 16) and the experimental group (online) lost 16.00
An elementary education researcher was interested in seeing how the color used to make corrections on students’ papers affected their self-esteem. He assembled first graders and asked them to take a third-grade math test. He told the first graders that the test would be very difficult for them
Given N = 73, α = .05, one-tailed, t expected to be negative, and t =−1.65, report the results in APA format.
Given N = 10 and t = 2.3147, report the results in APA format for a two-tailed test, α = .05.
If tcv = 2.396, write the decision rule for a one-tailed test for (a)when to reject the null hypothesis and (b) when to fail to reject the null hypothesis. (Hint: Contemplate the sig of tcv and what that means about what the researcher believes.)
There is a lot of evidence that fluoride reduces cavities but not all communities add it to their drinking water. A dentist, who expects to replicate this earlier work, classifies randomly selected communities in his state as (1) adding fluoride to their drinking water or (2) not adding fluoride to
A medical educator is using an independent-samples t test to compare the age of physicians who complete the minimum number of continuing education hours per year vs. those who complete extra hours of continuing education. (a) Write out H0 and H1 and (b)explain what they mean.
A clinical psychologist is studying the effects of an experimental medication on depression. He randomly assigns the next 50 patients at his clinic to receive either (a) Prozac or (b) a placebo. Each patient is treated individually. After eight weeks of treatment, each patient completes an
A demographer working for the U.S. Census Bureau wants to compare salaries for urban vs. rural areas. She gets a sample of psychologists who live in urban areas and a sample of psychologists who live in rural areas. From each, she finds out his or her annual income. What statistical test should she
One tests the ___assumption for the independent-samples t test by comparing the ___ of the two samples.
Researchers are often willing, for an independent-samples t test, to assume that the dependent variable is ___.
The ___assumption for the independent-samples t test says that the amount of variability in the two populations is about equal.
The ___assumption for the independent-samples t test is the one that allows a researcher to generalize the results back to the larger population.
The nonrobust assumption for an independent-samples t test is ___.
In order to use an independent-samples t test to analyze data from two samples, the samples have to be ___and one needs to know the ___for each sample.
___is the abbreviation for the total sample size in an independentsamples t test; ___ and ___are the abbreviations for the sizes of the samples in the two groups.
If the selection of cases for one sample determines the cases selected for the other sample, then the samples are ___samples.
If each sample in a two-sample t test is a random sample from its population, then the test is an ___-samples t test.
Two different types of two-sample t tests are the ___-samples t test and the ___-samples t test.
A classic experiment might use a two-sample t test to compare a ___group to an ___ group.
Two sample t tests use ___means to draw a conclusion about ___means.
Two sample t tests compare the ___of one sample to the ___of another sample.
To compute either a single-sample z test or a single-sample t test, one must know the population ___.
An exercise physiologist wondered whether doing one’s own chores(yard work, cleaning the house, etc.) had any impact on the resting heart rate. (A lower resting heart rate indicates better physical shape.)He wasn’t sure, for example, whether chores would function as exercise (which would lower
A dermatologist obtained a random sample of people who don’t use sunscreen and a random sample of people who use sunscreen of SPF 15 or higher. She examined each person’s skin using the Skin Cancer Risk Index, on which higher scores indicate a greater risk of developing skin cancer. For the 31
If M1 = 99, M2 = 86, and sM1−M2=8.64, calculata t.
If n1 = 12, s1 = 4, n2 = 16, and s2 = 3, calculate sPooled2 and sM1−M2.
Previous research has shown that people who have served in the U.S.Armed Forces feel more patriotic about America. A researcher obtains a sample of veterans and a sample of nonveterans, and administers the interval level Sense of Patriotism Scale (SPS). Higher scores on the SPS indicate greater
A nutritionist wants to compare calories for meals at restaurants with tablecloths to restaurants without tablecloths. He gets a sample of each type of restaurant and finds out the calorie count for the most popular meal at each restaurant. Should he use an independentsamples t test or a
A public health researcher wants to compare the rate of cigarette smoking for a sample of eastern states vs. a sample of western states.Should she use an independent-samples t test or a paired-samples t test?
A gym owner is offering a strength training course for women. Eight women have signed up. The gym owner measures how many pounds they can bench press at the first class. He plans to measure this again, 12 weeks later, at the last class, in order to see if their strength has changed. Should he use
Which confidence interval in Exercise 7.95 is wider: 90% or 99%?Explain why.
If N = 21 and sM = 1, write as much of the equation as possible for calculating the 90% CIμDiff and the 99% CIμDiff. Use Equation 7.4 as a guide.
If tcv for a two-tailed test with α = .05 is ± 2.228, what would the alpha level be for the critical value of 2.228 as a one-tailed test?
A researcher is conducting a two-tailed, single-sample t test with alpha set at .05. What is the largest value of t that one could have that, no matter how big N is, will guarantee failing to reject the null hypothesis?
to 7.95, what factors have an impact on a researcher’s ability to reject the null hypothesis? Which one(s) can he or she control?
Based on the answers to Exercises
A third researcher obtained two random samples from another population. The mean for this population is 50 (μ = 50). Each sample was the same size (N = 10) and each had the same standard deviation(s = 20). But one, sample E, had a mean of 80 (M = 80) and the other, sample F, a mean of 60 (M = 60).
Another researcher selected two random samples from one population. This population has a mean of 63 (μ = 63). It turned out that each sample had the same mean (M = 60) and standard deviation(s = 5). The only way the two samples differed was in terms of size:one, C, was smaller (N = 10) and one,
Imagine a researcher has taken two random samples from two populations (A and B). Each sample is the same size (N = 71), has the same sample mean (M = 50), and comes from a population with the same mean (μ = 52). The two populations differ in how much variability exists. As a result, one sample
Given the supplied information, interpret the results. A dean compared the GPA of a sample (N = 20) of students who spent more than two hours a night on homework (M =3.20, s = 0.50) to the average GPA at her college (μ = 2.80). She was curious if homework had any relationship, either positive or
Given the supplied information, interpret the results. A nurse practitioner has compared the blood pressure of a sample (N = 24) of people who are heavy salt users (M = 138, s = 16) to blood pressure in the general population (μ = 120) to see if high salt consumption were related to raised or
Given M = 55, μ = 50, tcv = ±2.093, and sM = 2.24, calculate the 95%confidence interval for the difference between population means.
Given M = 45, μ = 50, tcv = ±2.093, and sM = 2.24, calculate the 95%confidence interval for the difference between population means.
If N = 29 and t = 1.64, what is r 2?
Given N = 17 and t = 3.45, what is r 2?
Given M = 98, μ = 100, and s = 15, calculate Cohen’s d.
Given M = 90, μ = 100, and s = 15, calculate Cohen’s d.
Given N = 84 and t = 1.998, write the results in APA format.
Given N = 69 and t = 1.992, write the results in APA format.
Given N = 28 and t = 2.050, write the results in APA format. (p. 18)
Given N = 15 and t = 2.145, write the results in APA format. (p. 18)
If tcv = ±1.984 and t = − 1.00, is the null hypothesis rejected? (p. 18)
If tcv = ±2.776 and t = 1.12, is the null hypothesis rejected? (p. 18)
If tcv = ±2.030 and t = 2.16, is the null hypothesis rejected?
If tcv = ±2.012 and t = − 8.31, is the null hypothesis rejected? (p. 18)
If N = 25, M = 18, μ = 13, and s = 2, what is t?

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