A laboratory engineer describes an experiment in which the tensile strength of a synthetic fiber is of interest to themanufacturer. It is suspected that strength is related to the percentage of cotton in the fiber. Five levels of cottonpercentage are used, and five replicates are run in random order, resulting in the data below:ObservationsCotton (%)1234515771511920121712181825141818191930192522192335710111511Does cotton percentage affect breaking strength? Test the hypothesis at alpha 0.05F critical is Blank 1F stat is Blank 2Decision is to Blank 3 the null hypothesis. (accept or reject)

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Answered: A laboratory engineer describes an…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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We are testing whether a particular program of low impact exercise can improve the cholesterol level of stroke patients. We enroll a group of stroke patients in our study, and after six weeks we measure their serum cholesterol level in mmol/L, resulting in the following data: 6.1 9.3 6.3 4 9 5.5 6.3 4.2 4.7 7.8 4.3 7.5 9.1 4.2 6.9 8.1 5.6 9.4 8.3 8.8 7.2 5.7 6.5 3.8 3.8 9 9.4 4.5 8 7 4.5 9.4 6.6 4.1 6.6 9.1 3.9 5.3 (a) Construct a 95% confidence interval. _______< u < ______ From an existing study, we know that the average cholesterol level of all stroke patients is 7 mmol/L. We want to know if the level in our patients is significantly different from this. (b) What is our Test statistic? ______ (c) What is the two-tailed p-value of this result? ______
2. An experiment was conducted to determine whether four firing temperatures affect the density of brick. The experiment led to the following information Temperature 100 125 150 175 200 Total Grand Mean No. of Bricks (Reps) 3 4 4 3 4 18 Total Density 65.4 86.0 87.1 65.2 86.1 389.8 Mean Density 21.80 21.50 21.78 21.73 21.52 108.33 21.67 density=8441.82 a. At a=0.05, test whether the mean density of five firing temperatures are significantly different.
A community may be considered sociologically healthier the more variability there is in its housing values (up to a point). A major newspaper in one city investigated housing costs in several communities in its area and is running a story on its findings. For one of the communities, a random sample of 60 houses was examined, and the current market price of each house was determined. The newspaper published the following histogram summarizing these 60 prices. 20 15 10 5 0 Frequency 12 16 20 8 4 80 120 160 200 240 280 Current market price (in thousands of dollars) Based on this histogram, estimate the standard deviation of the sample of 60 prices. Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.
An experiment was conducted to investigate the effects of the concentrations of sulfuric acid (H₂SO4) and calcium chloride (CaCl₂) on the amount of black mud precipitate in the treatment of alkaline wastewater. There were three levels of each concentration, and two replicates of the experiment were made at each combination of levels. The relevant statistical analysis is provided in the following table. Source DF SS MS F P 2 457.65 228.83 8.845 0.008 H₂SO4 CaCl₂ 2 38783 19391 749.53 0.000 Interaction 4 279.78 69.946 2.704 0.099 Error 9 232.85 25.872 Total 17 39753 a) The appropriate statistical analysis to test would be: a. One-way ANOVA b. Two-way ANOVA C. Three-way ANOVA d. Two-Sample t-test b) Does there appear to be an interaction between concentration of sulfuric acid and calcium chloride at the .05 level? What does this say about the additive model? c) Can the effect of concentration of sulfuric acid on amount of black mud precipitate in the treatment of alkaline wastewater be…
Mr. Acosta, a sociologist, is doing a study to see if there is a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 adults revealed the following data. Test whether age and type of movie preferred are independent at the 0.05 level. Person's Age Movie 18-23 yr 24-29 yr 30-35 yr Row Total Drama 8 16 10 34 Science Fiction 10 8 12 30 Comedy 11 8 10 29 Column Total 29 32 32 93 (a) What is the level of significance?State the null and alternate hypotheses. H0: Age and movie preference are not independent.H1: Age and movie preference are independent.H0: Age and movie preference are independent.H1: Age and movie preference are independent. H0: Age and movie preference are not independent.H1: Age and movie preference are not independent.H0: Age and movie preference are independent.H1: Age and movie preference are not independent. (b) Find the value of the chi-square statistic for the sample. (Round…
Mr. Acosta, a sociologist, is doing a study to see if there is a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 adults revealed the following data. Test whether age and type of movie preferred are independent at the 0.05 level. Person's Age Movie 18-23 yr 24-29 yr 30-35 yr Row Total Drama 7 13 14 34 Science Fiction 11 11 8 30 Comedy 8 10 11 29 Column Total 26 34 33 93 (A) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)
Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: x 1 2 3 4 5 y 15.8 17.3 14.4 19.6 20.0 Σx = 15; Σy = 87.1; Σx2 = 55; Σy2 = 1,540.45; Σxy = 272 (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.) x = y = b = ŷ = + x (b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram. (c) Find the sample correlation coefficient r and the coefficient of determination r2. (Round your answers to three decimal places.) r = r2 = What percentage of variation in y is…
Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: x 1 2 3 4 5 y 15.8 17.3 14.4 19.6 20.0 Σx = 15; Σy = 87.1; Σx2 = 55; Σy2 = 1,540.45; Σxy = 272 (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.) x = y = b = ŷ = + x
2. A researcher had rats engage in a lever-press task for either a small, medium, or larger reward. The number of lever presses was the dependent variable. The data were as follows: Reward Size Small Medium Large 1 4 6 4 3 5 1 4 4 2 5 T = 13 SS = 2.75 T= 6 T= 20 SS = 9 SS = 2 EX2 = 165 a. Do the data indicate that reward size had a significant impact on lever-pressing? Use the hypothesis testing steps & p = .05. Compute any necessary post-hoc tests. b. Compute eta-squared to measure the effect size.
Prices of diamonds are very sensitive to their weight (measured in carat). For example, the price of a 1 carat diamond tends to be much higher than the price of a 0.99 carats diamond. To study this phenomenon in more detail, we consider two random samples of diamonds, 0.99 carats and 1 carat, each sample of size 23. The average price of 0.99 carats diamonds in the sample is $4451, while the average price of 1 carat diamonds in the sample is $5681. From long-term studies, we know that both the prices of 0.99 carats diamonds and the prices of 1 carat diamonds are normally distributed with standard deviations oj = $1332 (0.99 carats) and o2 = $1613 (1 carat), respectively. (a) Carry out a hypothesis test at significance level 0.01 to evaluate whether the true average price µi of 0.99 carats diamonds is lower than the true average price µ2 of 1 carat diamonds. Specify Ho and Ha, the test statistic, and calculate the p-value or use p-value considerations to conclude. (b) Compute the type II…
5. An article in Agricultural Engineering (December 1964, pp. 672-673) described an experiment in which the daily weight gain of swine is evaluated at different levels of housing temperature. The mean weight of each group of swine at the start of the experiment is considered to be a nuisance factor. The data from this experiment are as follows: Mean Weight (lbs) Housing Air Temperatures (°F) 100 50 60 70 80 90 1.37 1.58 2.00 1.97 1.40 100 0.39 150 1.47 1.75 2.16 1.82 1.14 -0.19 200 1.19 1.91 2.22 1.67 0.88 -0.77 Does housing air temperature affect mean weight gain at a = 0.05?
Mr. Acosta, a sociologist, is doing a study to see if there is a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 adults revealed the following data. Test whether age and type of movie preferred are independent at the 0.05 level. Person's Age Movie 18-23 yr 24-29 yr 30-35 yr Row Total Drama 9 13 12 34 Science Fiction 9 8 13 30 Comedy 10 8 11 29 Column Total 28 29 36 93 n USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Ho: Age and movie preference are independent. H: Age and movie preference are not independent. O Ho: Age and movie preference are independent. H,: Age and movie preference are independent. O Ho: Age and movie preference are not independent. H,: Age and movie preference are not independent. O Ho: Age and movie preference are not independent. H: Age and movie preference are independent. (b) Find the value of the chi-square statistic for the sample. (Round the…

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