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. 15 7 7 13 13 20 13 12 5 10 26 22 13 7 11 3 The sample mean is x = 12.3%. 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 α = 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.)

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…

. Each member of a large genetics class grows 12 pea plants from an independent pea family. Each family is expected to have 3/4 plants with smooth peas and 1/4 plants with wrinkled peas. a. On average, how many wrinkled pea plants will a student see in her 12 plants? b. What is the standard deviation of the proportion of wrinkled pea plants per student? c. What is the variance of the proportion of wrinkled pea plants per student? d. Predict what proportion of the students saw exactly two wrinkled pea plants in their sample.

4.A college student is interested in whether there is a difference between male and female students in the amount of time they spend studying each week period the student gathers information from a random sample of male and female students on campus. The amount of time spent studying is normally distributed. The data are: Male      Female 27          25 25           29           19           18 10           23           16           20 22           15 14           19   What statistical test should be done to analyze these data? Identify Ho and Ha for this study. Conduct the appropriate analysis. Should Ho be rejected? What should the researcher conclude? If significant, compute and interpret the effect size.

Listed below are amounts of arsenic in samples of brown rice from three different states. The amounts are in micrograms of arsenic and all samples have the same serving size. The data are from the Food and Drug Administration. Use a 0.05 significance level to test the claim that the three samples are from populations with the same mean. Assume that the  distributions for each state are normal and that all variances are equal.   Arkansas       4.8    4.9   5.0     5.4   5.4    5.4    5.6    5.6   5.6   5.9   6.0    6.1 California.     1.5     3.7    4.0    4.5   4.9    5.1     5.3    5.4   5.4   5.5   5.6    5.6 Texas.           5.6     5.8    6.6    6.9.  6.9    6.9    7.1     7.3    7.5    7.6   7.7     7.7