Exercise #2: Consider НA: μ Ho Compute the sample size required to achieve following power levels: a.) • σ = 25 · Effect size=5 • α = 5% · & = 80% b.) Same as above, but using 4 = 90% What happens to the required sample size when the power level is increased. c.) Same as in part a.) but using effect size = 15 What happens to the required sample size when the effect size is increased. d.) Same as in part a.) but using a = 10% What happens to the required sample size when the significance is increased. e.) For effect size = 5, what is the value of μA Q Search
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- Q4: In an experiment on a new drug for allergy, a sample of ten patients was selected and each given a dose (in milligrams) of the drug and the number of days of relief from allergy observed. The data obtained is given below: Dose ( r) 6 7 8 8 9 4 5 Days of relief (y )9 5 12 9 14 16 22 18 24 22 3 3 6 "= 59 Συ- 151Σ" = 39 Σύ - 651 Σ = 1003 (a) Find the equation of the least squares line. (b) Explain the meaning of the value of the slope you obtained in this problem. (c) Calculate and interpret the coefficient of determination. (d) Predict the number of days of relief for a patient who were given 8 milligrams of the drug. (e) Does the data indicate that the number of days of relief and the dose are positively correlated? (Use a = 0.05)Determine lz and oz from the parameters of the population and the sample size a. μ- 80, σ-4, η- 49 b. μ= 52 σ= 10, η = 21 C. H 27, o = 6, n = 15 Answer part a. Hi = ;O = part b. Hz = (two decimal places) part c. lz = ; στ (two decimal places)C-4) The concentration of active ingredient in a liquid laundry detergent is thought to be affected by the type of catalyst used in the process. Ten observations on concentration are taken with each catalyst, and the data follow: Catalyst 1: 57.9, 66.2. 65.4, 65.4, 65.2. 62.6, 67.6, 63.7, 67.2. 71.0 Catalyst 2: 66.4. 71.7. 70.3. 69.3, 64.8, 69.6, 68.6, 69.4, 65.3, 68.8. Find a 95% confidence interval on the ratio of active concentrations for the two catalysts, and explain it.
- Random collections of nine different solutions of a calcium compound were given to two laboratories, A and B. Each laboratory measured the calcium content (in mmol per liter) and reported the results. The data are paired by calcium compound. Compound 1 2 3 4 5 6 7 8 9 Lab A (x) 12.35 9.83 10.79 11.31 8.58 13.69 14.68 15.07 11.57 Lab B (y) 12.18 9.72 10.70 11.51 8.63 13.58 14.71 15.24 11.57 (a) Rank-order the data using 1 for the lowest calcium reading. Make a table of ranks to be used in a Spearman rank correlation test. Compound Lab A (x) Lab B (y) d = x − y d2 1 2 3 4 5 6 7 8 9 Σd2 = (b) Use a 5% level of significance to test for a monotone relation (either way) between ranks. Interpret the results. What is the level of significance? Compute the sample test statistic. (Round your answer to three decimal places.)Random collections of nine different solutions of a calcium compound were given to two laboratories, A and B. Each laboratory measured the calcium content (in mmol per liter) and reported the results. The data are paired by calcium compound. Compound 1 2 3 4 5 6 7 8 9 Lab A (x) 15.36 12.83 8.81 11.30 13.59 9.66 10.72 14.05 11.54 Lab B (y) 15.17 12.72 8.69 11.45 13.63 9.63 10.75 14.23 11.55 (a) Rank-order the data using 1 for the lowest calcium reading. Make a table of ranks to be used in a Spearman rank correlation test. (b) Compute the sample test statistic. (Round your answer to three decimal places.)estion 1. Exercise 10.3. Let X be the number of rolls of a fair die until I see the first six. Next, I choose a sample, with replacement, of size X from an urn with 5 red and 4 balls. Let Y be the number of green balls in my sample. green (a) Find EY X]. (b) Use your answer from part (a) to find EY. tion: English (India)
- An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Dr. Lewis believes the mean time for students at Clayton State University is longer than this average. A survey of 49 graduates from Clayton State had a mean time of 5.1 years to complete their Bachelor's degree, with a sample standard deviation of 1.2 years. Correctly identify the null and alternative hypotheses for this study:The table below presents the results of the test. 1) the researchers decide to use a 70-ms cutoff and obtain following tmredults: TP = 17, FP = 15, FN = 24, TN = 44. calculate the following values: a) sensitivity b) specificity c) PV (+) d) PV (-) 2) how did changing the cut-point affect the accuracy of the test?Fifty male subjects drank a measured amount x (in ounces) of a medication and the concentration y (in percent) in their blood of the active ingredient was measured 30 minutes later. The sample data are summarized by the following information: n = 50 Ex = 112.5 Ex? = 356.25 %3D Ey = 4.83 Ey = 0.667 Exy = 15.255 0 < x < 4.5 Or= 0.875 Or= 0.709 Or= -0.846 Or=0.460 Or= 0.965
- 4. (Exam 1 Summer 2020) Use the preamble below to answer the questions that follow An experiment to gain a better understanding of the role of various substances in melting ice was run in 2004 by Edinson Cavani, a researcher, in a certain lab in Memphis, TN. For each observation, a 10 ml block of ice was placed into water containing a given concentration of sugar, or salt, or a sugar and salt mix. The melting time for the ice block was measured in seconds and then converted to minutes. The three factors of interest were shape of ice block (lozenge, cylinder, and cube), solute (sugar, salt, and equal mix of sugar and salt), and concentration (5%, 10% 15%, 20%). (a) What is the response(outcome) variable for this study? Answer: (b) How many unique treatment combinations are there? Suppose there were two replicates per treatment combination, what is the total number of trials? i. Number of unique treatment combinations ii. Total number of trials Answer: Answer: (c) Would you say the…Let XXN(u. 16). How much should the sample size he for testing HeiH = 24 rs. He = 25 ata = 0.025 and ß = 0.409 (a) 77 (b) 48 (c) 35 (d) 28 (e) NoneThe minister of environment in a certain country decided to investigate whether expansion of a aluminum plant in that country would affect fluoride pollution in it's environment. The productions occurred the years 2005 and 2006. One of the things measured was the amount of fluoride in lamb jaws. The data available are measurements of fluoride in the jaws of 8 lambs that were slaughtered in the year 2004 and 8 lambs that were slaughtered in the year 2007. The data is shown below, along with a R output that can simplify your calculations. Fluoride amount 2004 (ug/g) | Fluoride amount 2007 (ug/g) 131.37 655.09 252.74 541.37 81.29 564.58 225.55 617.97 222.44 472.54 68.29 606.62 227.55 500.80 111.86 394.67 > fs2004 fs2007 mean (fs2004) [1] 165.1363 > mean (fs2007) [1] 544.205 > var (fs2004) [1] 5555.906 > var (fs2007) [1] 7348.022 > d mean (d) [1] 379.0688 > var (d) [1] 14657.70