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- a-dNationally, 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 13 22 13 13 7 12 23 19 11 9 13 4 The sample mean is x = 12.4%. 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? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: μ ≠ 11%; H1: μ = 11%; two-tailedH0: μ = 11%; H1: μ ≠ 11%; two-tailed H0: μ = 11%; H1: μ < 11%; left-tailedH0: μ = 11%; H1: μ > 11%; right-tailed (b) What sampling distribution will you…3. For a population with µ = 80 and o = 20, the distribution of sample means based on n = 16 will have an expected value of and a standard error of the mean of
- 9. Carboxy- hemoglobin is formed when hemoglobin is exposed to carbon monoxide. Heavy smokers tend to have a high percentage of carboxyhemoglobin in their blood (Reference: A Manual of Laboratory and Diagnostic Tests by F. Fischbach). Let x be a random variable rep- resenting percentage of carboxyhemoglobin in the blood. For a person who is a regular heavy smoker, x has a distribution that is approximately normal. A random sample of n-12 blood tests given to a heavy smoker gave the following results (percentage of carboxyhemoglobin in the blood): 9.1 9.5 10.2 9.8 11.3 12.2 11.6 10.3 8.9 9.7 13.4 9.9 Where = 10.49 and s = 1.36. A long-term population mean u -10% is considered a health risk. However, a long- term population mean above 10% is considered a clinical alert that the person may be asymptomatic. We will investigate the claim: the data indicate that the population mean percentage is higher than 10% for this patient? Use a = 0.05. a. Find the test statistic. b. Find the critical…16. Standardized test scores are normally distributed with an average of 500 and a variance of 100. What is the chance that a score is between 485 and 550? A. 0.2511 B. 0.3520 C. 0.6554 D0.93321. Tim Hortons wanted to estimate the difference in the mean amounts of caffeine in two brands of coffee. They took a sample of 18-lbs jars of Brand I and another sample of 13-lbs jars of Brand II coffee. The following summary data (sample statistics) are collected? nį = 10 x, = 23 S1 = 3 Brand I Brand II n2 = 12 x2 = 25 S2 = 4 Assume that the two populations are normally distributed. A. Test at 5 % level of significance, whether there is a difference in the mean amounts of caffeine between the 2 brands of coffee. B. Construct a 95% Confidence Interval to estimate the difference in the mean amounts of caffeine in 2 brands of coffee. C. Does the result in part b) confirm your findings from part a)?
- disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 223 numerical entries from the file and r = 48 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1.(i) Test the claim that p is less than 0.301. Use ? = 0.05. (a) What is the level of significance?State the null and alternate hypotheses. H0: p < 0.301; H1: p = 0.301H0: p = 0.301; H1: p > 0.301 H0: p = 0.301; H1: p < 0.301H0: p = 0.301; H1: p ≠ 0.301 (b) What sampling distribution will you use? The standard normal, since np > 5 and nq > 5. The standard normal, since np < 5 and nq <…4. For a population with a µ = 72 and o = 20. What is the probability of obtaining a sample mean greater than 75 a. for a random sample of N = 100 scores? b. for a random sample of N = 225 scores?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…
- 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.)Suppose the horses in a large stable have a mean weight of 818 lbs, and a variance of 3481. What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 18 lbs if 34 horses are sampled at random from the stable? 0.920 0.925 0.912 O 0.945 None of these tA pathologist has been studying the frequency of bacterial colonies within the field of a microscope using samples of throat cultures from healthy adults. Long-term history indicates that there is an average of 2.80 bacteria colonies per field. Let r be a random variable that represents the number of bacteria colonies per field. Let O represent the number of observed bacteria colonies per field for throat cultures from healthy adults. A random sample of 100 healthy adults gave the following information. 2 3 4 5 or more 13 18 28 16 17 8 (a) The pathologist wants to use a Poisson distribution to represent the probability of r, the number of bacteria colonies per field. The Poisson distribution is given below. P(r) = r! Here 1 = 2.80 is the average number of bacteria colonies per field. Compute P(r) for r = 0, 1, 2, 3, 4, and 5 or more. (Round your answers to three decimal places.) P(0) = P(1) = Р(2) Р(3) 3 P(4) = %3D P(5 or more) = (b) Compute the expected number of colonies E = 100P(r)…
