Concept explainers
Suppose that
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An Introduction to Mathematical Statistics and Its Applications (6th Edition)
- Assume that ρxy = .30 between weight and exercise for the population of normal adults. However, a researcher believes the relationship is stronger for children. The researcher tests a sample of 28 children and obtains an rxy = .47. Does this result support the researcher’s belief? Conduct an appropriate statistical test using an alpha level of .05.arrow_forward1. A researcher reports an F-ratio with df(between) = 3 and df(within) = 28. How many treatment conditions were compared in the experiment? If samples have an equal number of participants, how many are in each treatment? 2. A researcher obtains an F = 4.10 with df = 2, 14. Is this value sufficient to reject the null with α = .05? Is it sufficient enough to reject the null with α = .01?arrow_forwardSuppose the proportion X of surface area in a randomly selected quadrat that is covered by a certain plant has a standard beta distribution with ? = 4 and ? = 2. (a) Compute E(X) and V(X). (Round your answers to four decimal places.) E(X) = V(X) = (b) Compute P(X ≤ 0.3). (Round your answer to four decimal places.)(c) Compute P(0.3 ≤ X ≤ 0.7). (Round your answer to four decimal places.)arrow_forward
- Is there a way to solve this w/o using L'Hospital's rule?arrow_forwardThe tests of assumptions for yield gave values for Levene’s statistic and Shapiro-Wilk’s as 0.0562 and .00271, respectively. At a=0.05 , which statistical test is most appropriate to compare the yield among the nitrogen rates? a. Cochran’s Q B. Friedman’s C. Kruskal Wallis test . D. Anova F-testarrow_forward1. Let ?(?) = 3 cos(?) + ? −? + 4. a. [4 pts] Compute the average value of ?(?) on [0,1]. b. [4 pts] Compute the average value of ?(?) on [0,10]. c. [6 pts] Compute the average value of ?(?) on [0, ?], for a general positive constant b. d. [6 pts] Take the limit of your expression from part c as ? → ∞. What does that say about the long-term behavior of ?(?)?arrow_forward
- The diameter of a metal shaft used in a disk-drive unit is normally distributed with mean 0.2508 in. and std. dev. 0.0005 in. The specification on the shaft have been established as (0.25-0.0015 in, 0.25+0.0015in) If the process mean has been adjusted to 0.25 in, what fraction of the shafts produced does NOT conform to specifications? a). 0.0027 b). 0.0013 c).0.08 d). 0.16arrow_forwardLet W ~ Gamma(100, 3.4). (a) Give the exact value of P(1.5 < W < 5.0) (b) Give the approximate value of P(1.5 < W < 5.0) using normal approximationarrow_forwardA researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster. Use the definitions of X1 and X2 as given in the table. Consequently, D=X1=X2What critical value should be used at a-0.05?arrow_forward
- Can you find the amount of salt A in the tank at any time t?arrow_forwardA sample is counted for 10 minutes and results in 530 gross counts. A 30-minute background count results in 1,500 counts. The detector efficiency is 0.10 cpm/dpm. What is the critical level (net count rate) that corresponds to a risk of making a Type I error, where α is 0.05? a. 3.0 cpm b. 4.2 cpm c. 50 cpm d. 53 cpmarrow_forwardwe investigate if a period of time feels longer or shorter when people are bored compacted to when they are not bored. using independent samples, we obtain these estimates of the time period (in minutes) sample 1 (bored) xbar= 14.5 s2x= 10.22 n= 28 sample 2(not bored) xbar=9.0 s2x=14.6 n=34 (a) what are Ho and Ha? (b) compute t-obt (c) with alpha =.05, what is t-crit?arrow_forward
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,