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About 102926 results. 1294 free access solutions
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| m102810 | This is a technique to break down the variation of a random variable into useful components (called stratum) in order to decrease experimental variation and increase accuracy of results. It has been found that a more accurate estimate of population mean m can often be obtained by taking measurements from naturally occurring subpopulations and combining the results using weighted averages. For example, suppose an accurate estimate of the mean weight of sixth grade students is desired for a large school system. Suppose (for cost reasons) we can only take a random sample of m = 100 students, Instead of taking a simple random sample of 100 students from the entire population of all sixth grade students, we use stratifi ed sampling as follows. The school system under study consists three large schools. School A has N1 = 310 sixth grade students, School B has N2 = 420 sixth grade students, and School C has N3 = 516 sixth grade students. This is a total population of 1246 sixth grade students in our study and we have strata consisting of the 3 schools. A preliminary study in each school with relatively small sample size has given estimates for the sample standard deviation s of sixth grade student weights in each school. These are shown in the following table.
How many students should we randomly choose from each school for a best estimate m for the population mean weight? A lot of mathematics goes into the answer. Fortunately, Bill Williams of Bell Laboratories wrote a book calle |
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| m102811 | This problem continues the Focus Problem. The solution involves applying several basic probability rules and a little algebra to solve an equation.
(a) If the polygraph of Problem 27 indicated that 30% of the questions were answered with lies, what would you estimate for the actual percentage of lies in the answers? Let B = event detector indicates a lie. We are given P (B) = 0.30. Let A = event person is lying, so Ac = event person is not lying. Then
P (B) = P (A and B) + P (Ac and B)
P (B) = P (A) P (B | A) + P (Ac) P (B | Ac)
Replacing P (Ac) by 1 - P (A) gives
P (B) = P (A) ( P (B | A) + [1 - P (A)] ( P (B | Ac)
Substitute known values for P (B), P (B | A), and P (B | Ac) into the last equation and solve for P (A).
(b) If the polygraph indicated that 70% of the questions were answered with lies, what would you estimate for the actual percentage of lies? |
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| m102812 | This problem is based on information taken from Life in America s Fifty States by G. S. Thomas. A random sample of n1 = 153 people ages 16 to 19 was taken from the island of Oahu, Hawaii, and 12 were found to be high school dropouts. Another random sample of n2 = 128 people ages 16 to 19 was taken from Sweetwater County, Wyoming, and 7 were found to be high school dropouts. Do these data indicate that the population proportion of high school dropouts on Oahu is different (either way) from that of Sweetwater County? Use a 1% level of signifi cance.
(a) What is the level of signi ficance? State the null and alternate hypotheses.
(b) What sampling distribution will you use? What assumptions are you making? Compute the sample test statistic and corresponding z or t value as appropriate.
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically signifi cant at level a?
(e) Interpret your conclusion in the context of the application.
For degrees of freedom d.f. not in the Student s t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and therefore produce a slightly more "conservative" answer.
Answers may vary due to rounding. |
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| m102813 | This problem shows you how to make a better blend of almost anything.
Let x1, x2, ... xn be independent random variables with respective variances (21, (22 , ... , (2n.
Let c1, c2, .........., cn be constant weights such that 0 ( ci ( 1 and c1 + c2 + ... + cn = 1. The linear combination w = c1x1 + c2 x2 + ... + cnxn is a random variable with variance
(a) Two types of epoxy resin are used to make a new blend of superglue. Both resins have about the same mean breaking strength and act independently. The question is how to blend the resins (with the hardener) to get the most consistent breaking strength. Why is this important, and why would this require minimal (2W?
We don t want some bonds to be really strong while others are very weak, resulting in inconsistent bonding.
Let x1 and x2 be random variables representing breaking strength (lb) of each resin under uniform testing conditions. If (1 = 8 lb (2 = 12 lb, show why a blend of about 69% resin 1 and 31% resin 2 will result in a superglue with smallest (W2 and most consistent bond strength.
(b) Use c1 = 0.69 and c2 = 0.31 to compute (w and show that (w is less than both s1 ands2. The dictionary meaning of the word synergetic is "working together or cooperating for a better overall effect." Write a brief explanation of how the blend w = c1x1 + c2 x2 has a synergetic effect for the purpose of reducing variance? |
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| m102814 | This problem will be referred to in the study of control charts (Section 6.1). In the binomial probability distribution, let the number of trials be n = 3, and let the probability of success be p = 0.0228. Use a calculator to compute
(a) The probability of two successes.
(b) The probability of three successes.
(c) The probability of two or three successes. |
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| m102815 | Three events A, B, and C are said to be independent if
P(A & B) = P(A) · P(B),
P(A & C) = P(A) · P(C),
P(B & C) = P(B) · P(C), and
P(A & B & C) = P(A) · P(B) · P(C).
What is required for four events to be independent? Explain your definition in words. |
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| m102816 | Three grades of jet fuel are blended to be used on long commercial flights. Each grade cost about the same and has about the same ignition or burn rate (gal/min) in a jet engine. The question is how to make the blend for the most consistent ignition rate. Assume the ignition rates of the three grades of fuel are statistically independent.
(a) Let x1, x2, x3 be random variables representing ignition rate (gal/min) for the three grades of fuel. After extensive testing (flying under different conditions) the standard deviations are found to be (1 = 7, (2 = 12 and (3 = 15. Explain why a blend of approximately 64% grade 1 fuel with 22% grade 2 fuel and 14% grade 3 fuel would give the most consistent ignition rate.
(b) Use c1 = 0.64, c2 = 0.22, and c3 = 0.14 to compute (w and show that (w is less than each of (1, (2 and (3. Would you say the blended jet fuel has a more consistent ignition rate than each separate fuel? Explain. |
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| m102817 | Three local districts are "swing" districts for an upcoming election on a contentious political issue. A survey will be conducted in which voters will be asked to rate their opinion regarding this issue on a scale of 0 (strongly oppose) to 10 (strongly support). A small preliminary random sample from each district was used to estimate the sample standard deviation s of responses for the district. The following table shows the number of voters N in each district and the sample standard deviation s of strength of support in each district.
District 1 __________ District 2 __________ District 3
N1 = 1525 .............. N2 = 917 .............. N3 = 2890
s1 = 2.2 .................. s2 = 1.4 .................. s3 = 3.3
We have a total population of 5332 voters and 3 strata (districts). The group doing the survey has enough funding to obtain a random sample of m = 250 total responses from all the districts.
(a) Compute the size of the random samples n1, n2, n3 to taken from each district. Round each sample size to the nearest whole number and make sure they add up to m = 250.
(b) Suppose you took the appropriate random samples from each district and you got the following average political support measures (scale 0 to 10): x̅1 = 6.2, x̅2 = 3.1 x̅3 = 8.5. Compute your best estimate for the population mean m (scale 0 to 10) of voter support for the issue from the total population of these three districts. |
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| m102818 | To better understand eating patterns that might contribute to obesity, a researcher measures the average number of calories (per meal) consumed by shift workers (morning, afternoon, night) during two seasons (summer and winter). The hypothetical results are given in the following table.
(a) Complete the F table and make a decision to retain or reject the null hypothesis for each hypothesis test.
(b) Explain why post hoc tests are not necessary. |
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| m102819 | To compare two elementary schools regarding teaching of reading skills, 12 sets of identical twins were used. In each case, one child was selected at random and sent to school A, and his or her twin was sent to school B. Near the end of fifth grade, an achievement test was given to each child. The results follow:
Use a 0.05 level of signifi cance to test the hypothesis that the two schools have the same effectiveness in teaching reading skills against the alternate hypothesis that the schools are not equally effective.
(a) What is the level of signi ficance? State the null and alternate hypotheses.
(b) Compute the sample test statistic. What is the sampling distribution?
(c) Find the P-value of the sample test statistic.
(d) Conclude the test.
(e) Interpret the conclusion in the context of the application. |
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| m102820 | To demonstrate flavor aversion learning (that is, learning to dislike a flavor that is associated with becoming sick), researchers gave one group of laboratory rats an injection of lithium chloride immediately following consumption of saccharin-flavored water. Lithium chloride makes rats feel sick. A control group was not made sick after drinking the flavored water. The next day, both groups were allowed to drink saccharin-flavored water. The amounts consumed (in milliliters) for both groups during this test are given below.
(a) Test whether or not consumption of saccharin-flavored water differed between groups using a .05 level of significance. State the value of the test statistic and the decision to retain or reject the null hypothesis.
(b) Compute effect size using eta-squared (η2). |
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| m102821 | To test the relationship between sex and responsiveness to feedback, a group of men and women were given a vignette describing a person of the opposite sex who gave negative, positive, or neutral feedback about relationship advice. Participants rated how positively they felt about the individual described in the vignette, with higher ratings indicating more positive feelings.
(a) Complete the F table and make a decision to retain or reject the null hypothesis for each hypothesis test.
(b) Based on the results you obtained, what is the next step? |
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| m102822 | To test whether animal subjects consume the same amounts of sweet-tasting solutions, a researcher has 10 subjects consume one of three sweet-tasting solutions: sucrose, saccharin, or Polycose. The amount consumed (in milliliters) of each solution is given in the table.
(a) Complete the F table.
(b) Compute Tukey s HSD post hoc test and interpret the results. |
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| m102823 | To test whether arousal or stress levels increase as the difficulty of a task increases, 10 participants were asked to complete an easy, typical, or difficult task. Their galvanic skin response (GSR) was recorded. A GSR measures the electrical signals of the skin in units called micro Siemens (μS), with higher signals indicating greater arousal or stress. The data for each task are given in the table.
(a) Complete the F table.
(b) Compute Fisher s LSD post hoc test and interpret the results. |
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| m102824 | To test whether students in a higher grade level would be less disruptive in class, a school psychologist recorded the number of documented interruptions during one day of classes from nine local high schools. The sample consisted of nine freshman, sophomore, junior, and senior high school classes. The data for each high school class are given in the table.
(a) Complete the F table.
(b) Is it necessary to compute a post hoc test? Explain. |
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| m102825 | Tri-County Bank is a small independent bank in central Wyoming. This is a rural bank that makes loans on items as small as horses and pickup trucks to items as large as ranch land. Total monthly loan requests are used by bank of ficials as an indicator of economic business conditions in this rural community. The mean monthly loan request for the past several years has been 615.1 (in thousands of dollars) with a standard deviation of 11.2 (in thousands of dollars). The distribution of loan requests is approximately mound-shaped and symmetric.
(a) For 12 months, the following monthly loan requests (in thousands of dollars) were made to Tri-County Bank:
Make a control chart for the total monthly loan requests, and plot the preceding data on the control chart. Interpretation From the control chart, would you say the local business economy is heating up or cooling down? Explain your answer by referring to any trend you may see on the control chart. Identify all out-of-control signals by type (I, II, or III).
(b) For another 12-month period, the following monthly loan requests (in thousands of dollars) were made to Tri-County Bank:
Make a control chart for the total monthly loan requests, and plot the preceding data on the control chart. Interpretation From the control chart, would you say the local business economy is heating up, cooling down, or about normal? Explain your answer by referring to the control chart. Identify all out-of-control signals by type (I, II, or III) |
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| m102826 | Tung and Deng (2007) studied how emoticons (computerized facial expressions) and sex influenced intrinsic motivation to complete a computer task. Emoticons were used as feedback for responses during the task. These faces were either static (presented still for the duration of feedback) or dynamic (presented as a neutral face and changed to the expression corresponding to the feedback). The researchers conducted a 2 × 2 between-subjects ANOVA, with emoticon style (static, dynamic) and sex as the factors. The F table gives the data reported in the study.
(a) Is a significant main effect or interaction evident in this study and, if so, for which factor?
(b) Are post hoc tests required? Explain. |
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| m102827 | Tunney (2006) was interested in various probability relationships. Specifically, he was interested in how the presentation of probabilities (either as a probability or as a frequency) influenced participant choices. The following is an example of how he presented bets for frequency and probability. Both statements say the same thing for each bet but in different ways.
Based on this table,
(a) What is the mathematical expectation for winning the Pbet,
(b) What is the mathematical expectation for winning the £-bet? Based on the mathematical expectation of making P-bets and £-bets,
(c) If you had to make one bet, which one would you make? Explain. |
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| m102828 | Turbid water is muddy or cloudy water. Sunlight is necessary for most life forms; thus turbid water is considered a threat to wetland ecosystems. Passive filtration systems are commonly used to reduce turbidity in wetlands. Suspended solids are measured in mg/L. Is there a relation between input and output turbidity for a passive fi ltration system and, if so, is it statistically signifi cant? At a wetlands environment in Illinois, the inlet and outlet turbidity of a passive filtration system have been measured. A random sample of measurements follow.
(i) Rank-order the inlet readings using 1 as the largest data value. Also rank-order the outlet readings using 1 as the largest data value. Then construct a table of ranks to be used for a Spearman rank correlation test.
(ii) Use a 1% level of signi ficance to test the claim that there is a monotone relation ship (either way) between the ranks of the inlet readings and outlet readings.
(a) What is the level of signi ficance? State the null and alternate hypotheses.
(b) Compute the sample test statistic.
(c) Find or estimate the P-value of the sample test statistic.
(d) Conclude the test.
(e) Interpret the conclusion in the context of the application. |
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| m102829 | Twenty-two fourth-grade children were randomly divided into two groups. Group A was taught spelling by a phonetic method. Group B was taught spelling by a memorization method. At the end of the fourth grade, all children were given a standard spelling exam.
The scores are as follows.
Use a 1% level of signifi cance to test the claim that there is no difference in the test score distributions based on instruction method.
(a) What is the level of signifi cance? State the null and alternate hypotheses.
(b) Compute the sample test statistic. What is the sampling distribution?
What conditions are necessary to use this distribution?
(c) Find the P-value of the sample test statistic.
(d) Conclude the test.
(e) Interpret the conclusion in the context of the application. |
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