When an experiment has a completely randomized design, a. experimental units are randomly assigned to each combination of levels of two factors.   b. independent, random samples of experimental units are assigned to the treatments.   c. the randomization occurs only within blocks.

A random sample of eight pairs of twins was randomly assigned to treatment A or treatment B. The data are given in the following table.Twins :            1      2      3      4      5      6    7      8Treatment A: 48.3 44.6 49.7 40.5 54.3 55.6 45.8 35.4Treatment B: 43.5 43.8 53.7 43.9 54.4 54.7 45.2 34.4a. Is there significant evidence that the two treatments differ using an α = 0.05 paired t test.b. Place a 95% confidence interval on the mean difference between the responses from the two treatments.

3.  Can SAT scores predict college performance?  Let x be a variable that represents SAT score of a computer science major, and let y be a variable that represents a student’s GPA upon graduation.  A random sample of n =15 computer science majors provided their SAT scores and GPAs: x 1232 1070 1086 1287 1130 1048 1121 1095 1135 1208 1333 1160 1186 1243 1261 y 3.52 2.91 2.4 3.47 3.47 2.37 2.4 2.24 3.02 3.32 3.59 2.54 3.19 3.71 3.58   The scatter diagram for the SAT score and GPA is given below:   (a)  Find the sample correlation coefficient r.  Truncate to two decimal places.  What does the value tell you about the data? (b)  Find the equation of the least squares line .  Truncate to four decimal places.  What does the slope mean? (c)  Find the value of the coefficient of determination .  Truncate to two decimal places.  What does this number mean? (d)  What is the predicted GPA if a computer science major got a…

1. Many supermarket chains are working to reduce the amount of arsenic in the chicken they sell. To accomplish this, one chain plans to measure, for each supplier, the amount of arsenic in a random sample of chickens. The chain will cancel its relationship with a supplier if the sample provides sufficient evidence that the average amount of arsenic in chicken provided by that supplier is greater than 80 ppb (parts per billion). A randomization distribution for testing VS is shown below. 40 30 20 10 60 Left Tail Two-Tail Right Tail 70 80 null = 80 90 100 L samples = 500 mean = 80.026 std. error = 8.327 110 (d) For each supplier, the supermarket chain has to decide whether or not to cancel its relationship with the supplier, based on the average amount of arsenic found in the sample of chicken from that supplier. Describe what a Type I error would be in this situation. What would be the consequences? (e) Describe how a Type II error might occur. What would be the consequences?

Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail. 16 6 8 9 10 18 14 13 9 10 25 18 13 8 14 3 The sample mean is x = 12.1%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and σ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use ? = 0.01. (a) What is the level of significance?   Compute the z value of the sample test statistic. (Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

Hospital floors: Hospital floors are usually bare tiles instead of carpet. Carpets will decrease noise but might increase germ growth.   To study this, researchers installed carpet in 8 of 16 hospital rooms. They randomly selected the rooms to carpet. The other rooms had bare tiles. After two weeks of normal use, they collected air samples from the rooms and counted the bacteria in each sample.   Based on this description of the experiment, which of the following is a part of the experiment design? Check all that apply.   Group of answer choices

Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year many small plots of equal size but different soil/fertilizer conditions are planted with wheat. At the end of the growing season, the yield (in pounds) of the wheat on the plot is measured. Suppose for a random sample of years, one plot gave the following annual wheat production (in pounds):  3.81 2.97 5.19 3.40 3.05 2.40 4.35 3.00 4.89 5.23 3.37 4.00 3.84 5.42 5.09 5.03 For this plot, the sample variance is . Another random sample of years for a second plot gave the following annual wheat production (in pounds):  3.53 3.65 3.89 4.19 3.44 3.42 3.58 3.83 3.46 4.32 3.58 3.45 3.77 3.54 3.48 4.07 For this plot, the sample variance is . Test the claim using  that the population variance of annual wheat production for the first plot is larger than that for the second plot.  Find (or estimate) the P-value of the sample…