A group of researchers wanted to determine if there was a difference in the predation habits of cougars upon adult male Homo sapiens at two unique watering holes. Using the following data, determine if there is a difference between the two watering holes.
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- The following output was obtained from a computer program that performed a two-factorANOVA on a factorial experiment. Two-way ANOVA: y versus A, BSource DF SS MS F PA 1 0.322 ? ? 0.8513B ? 80.554 40.2771 4.59 0.0331Interaction ? ? ? ? 0.1167Error 12 105.327 8.7773Total 17 231.551 (a) Fill in the blanks in the ANOVA table.A researcher wants to know if the time spent in prison for a particular type of crime was the same for men and women. A random sample of men and women were each asked to give the length of sentence received. The data, in years, are listed to the right. Use the Wilcoxon rank sum test to find R, the sum of the ranks for the smaller sample, to test the claim that there is no difference in the sentence received by each gender. Men 10 22 16 18 19 26 Women 9 12 9 14 26 12 Men 14 22 12 19 23 24 Women 34 8 10 13 17 27 A. 125.5 B. 115.5 C. 173.5 D. 155.5The table below contains the total cost ($) for four tickets to a basketball game purchased on the secondary market, two beers, two soft drinks, two hot dogs, and one parking space at each arena during a recent season. 298.97364.59427.79213.23307.54531.23297.49302.56521.19291.69366.83532.67230.38320.12507.88212.87452.34656.21245.26436.92709.57220.91485.82727.63365.07487.58788.14360.31467.92886.93 a. Organize these costs as an ordered array. b. Construct a frequency distribution and a percentage distribution for these costs. c. Around what values, if any, are at least 75% of the costs of attending the game concentrated? Explain.
- An alloy manufacturer is investigating if they can improve the strength of one of their alloysby producing it at a lower temperature. To investigate that, they produce the alloy at twodifferent temperatures (high and low) and then measure the breaking strength of randomsamples of specimens from each. The following table represents the strength of the randomsamples at the higher and lower temperature, in units of 0.001-inch deflection. Temp. Strength (0.001 inch)High 87 64 66 85 76 49 97 73 75 77 69 68 89 27 58 84Low 88 82 81 85 79 80 88 78 77 85 79 76 Do the results support the hypothesis that lowering the production temperature can improve thestrength of the alloy, with 95% confidence? (Hint: Don’t forget investigating variances. Use 98% confidence for that.)Benford's Law states that the first nonzero digits of numbers drawn at random from a large complex data file have the following probability distribution.† First Nonzero Digit 1 2 3 4 5 6 7 8 9 Probability 0.301 0.176 0.125 0.097 0.079 0.067 0.058 0.051 0.046 Suppose that n = 275 numerical entries were drawn at random from a large accounting file of a major corporation. The first nonzero digits were recorded for the sample. First Nonzero Digit 1 2 3 4 5 6 7 8 9 Sample Frequency 75 48 37 26 25 18 13 17 16 Use a 1% level of significance to test the claim that the distribution of first nonzero digits in this accounting file follows Benford's Law. (b) 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.) What are the degrees of freedom?Benford's Law states that the first nonzero digits of numbers drawn at random from a large complex data file have the following probability distribution.† First Nonzero Digit 1 2 3 4 5 6 7 8 9 Probability 0.301 0.176 0.125 0.097 0.079 0.067 0.058 0.051 0.046 Suppose that n = 275 numerical entries were drawn at random from a large accounting file of a major corporation. The first nonzero digits were recorded for the sample. First Nonzero Digit 1 2 3 4 5 6 7 8 9 Sample Frequency 88 46 30 25 22 18 13 17 16 State the null and alternate hypotheses. H0: The distributions are different.H1: The distributions are the same.H0: The distributions are the same.H1: The distributions are the same. H0: The distributions are the same.H1: The distributions are different.H0: The distributions are different.H1: The distributions are different. (b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the…
- An insurance company offers its policyholders a number of differentpremium payment options. For a randomly selected policyholder, let X=the number of months between successive payments. The cdf of X is asfollows:(attached) a. What is the pmf of X?b. Using just the cdf, compute P(3≤ x ≤6) and P(4 ≤ X).Nationally, at least 60% of Ph.D. students have paid assistantships. A collegedean feels that this is not true in his state, so he randomly selects 50 Ph.D.students and finds that 26 have assistantships. At α = 0.05, is the deancorrect?Marine biologists have noticed that the color of the outermost growth band on a clam tends to be related to the time of year in which the clam dies. A biologist conducted a small investigation of whether this is true for the species Protothaca staminea. She collected a sample of 55 clam shells in February and 55 clam shells in March. 14 of the shells from February had a dark color on the outermost growth band, whereas 8 of the shells from March had a dark color on the outermost growth band. Carry out a hypothesis test to see if there is a difference in the proportion of shells with a dark outermost growth band between the two months; specifically, if the population proportion in February is higher than March. Let ? = 0.1.Note: Do all calculations as February - MarchA) The point estimate for the true difference in proportion of dark growth bands between February and March is: Note: answer using 4 decimal precisionB) The test statistic, ztest, is: Note: answer using 2 decimal…
- An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholder, let X = the number of months between successive payments. The cdf of X is as follows: REFER IMAGE a. What is the pmf of X?b. Using just the cdf, compute P(3 ≤ x ≤ 6) and P(4 ≤ X)Is it possible to make a X-Bar and R control chart without a data set? I'm told to solve it by hand, but am unsure of how to do that with only the summation notationAccording to a recent marketing campaign, drinkers of either Diet Coke or Diet Pepsi participated in blind taste tests to see which of the drinks was their favorite. In one Pepsi television commercial, an anouncer states that "in recent blind taste tests, at least one half of the surveyed preferred Diet Pepsi over Diet Coke." Suppose that in one of those taste tests, 5050 out of the 120120 participating preferred Diet Pepsi. Test the hypothesis, using α=0.05α=0.05 that at least half of all participants will select Diet Pepsi in a blind taste (hint: take HaHa to be that fewer than half prefer Diet Pepsi) test by giving the following:(a) the test statistic Recall the zz value that marks the start of the rejection region is the critical zz score; if you're lower tailed, it's the zz value that has left area of αα; if you're right tailed, it's the zz value whose area to the right is αα; if you're two-tailed, they're the values of the ±z±z value that −z−z has left area of α2α2 and zz…