An article in the Journal of the American Statistical Association (1990, Vol. 85, pp. 972–985) measured the weight of 30 rats under experiment controls. Suppose that 12 were underweight rats. (a) Calculate a 95% two-sided confidence interval on the true proportion of rats that would show underweight from the experiment. (b) Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.02? (c) How large must the sample be if you wish to be at least 95% confident that the error in estimating p is less than 0.02, regardless of the true value of p?
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An article in the Journal of the American Statistical
Association (1990, Vol. 85, pp. 972–985) measured the weight
of 30 rats under experiment controls. Suppose that 12 were
underweight rats.
(a) Calculate a 95% two-sided confidence interval on the true
proportion of rats that would show underweight from the
experiment.
(b) Using the point estimate of p obtained from the preliminary
sample, what
the error in estimating the true value of p is less than 0.02?
(c) How large must the sample be if you wish to be at least
95% confident that the error in estimating p is less than
0.02, regardless of the true value of p?
Step by step
Solved in 4 steps
- The critical value (z -score) for an 84% confidence interval for a two tailed test is approximately 0.995 1.405 1.965 2.650A study of 420,045 cell phone users found that 130 of them developed cancer of the brain or nervous system. Prior to this study of cell phone use, the rate of such cancer was found to be 0.0332% for those not using cell phones. Complete parts (a) and (b). a. Use the sample data to construct a 90% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system. nothing%<p<nothing% (Round to three decimal places as needed.) b. Do cell phone users appear to have a rate of cancer of the brain or nervous system that is different from the rate of such cancer among those not using cell phones? Why or why not? A. YES, because 0.0332% is not included in the confidence interval b. no, because 0.0332% is not included in the confidence interval c. yes, because 0.0332% is included in the confidence interval d. no, because 0.0332% is included in the confidence intervalA study of 420,072 cell phone users found that 135 of them developed cancer of the brain or nervous system. Prior to this study of cell phone use, the rate of such cancer was found to be 0.0336% for those not using cell phones. Complete parts (a) and (b). a. Use the sample data to construct a 95% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system. D%(b) The strengths of stainless steel and carbon steel are being compared. Random samples were selected and tested. Table Q3 shows the tensile strengths (in MPa) of the steel samples. Construct a 95% confidence interval for the difference between the means of the two steel samples. TABLE Q3: Tensile strength of stainless steel and carbon steel Steel Type Tensile Strength (MPa) Stainless Steel 520 456 497 425 504 448 470 Carbon Steel 394 410 432 380 416A study of 420,092 cell phone users found that 134 of them developed cancer of the brain or nervous system. Prior to this study of cell phone use, the rate of such cancer was found to be 0.0322% for those not using cell phones. Complete parts (a) and (b). a. Use the sample data to construct a 95% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system. %In an engineering class, students want to determine the difference in the mean strength between two different types of building materials—Type A, which is relatively inexpensive, and Type B, which is slightly more expensive. The students take a random sample of 60 of the Type A building material and a random sample of 27 of the Type B building material. Given the mean strength for each sample, the students construct a 95% confidence interval for the difference in population means. (a) Determine the degrees of freedom for the conservative approach for finding the t critical value. (b) Find the t critical value associated with 95% confidence. (Use a table or SALT. Round your answer to two decimal places.)A study of 420,082 cell phone users found that 136 of them developed cancer of the brain or nervous system. Prior to this study of cell phone use, the rate of such cancer was found to be 0.0415% for those not using cell phones. Complete parts (a) and (b). a. Use the sample data to construct a 90% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system. %A study of 420,073 cell phone users found that 136 of them developed cancer of the brain or nervous system. Prior to this study of cell phone use, the rate of such cancer was found to be 0.0326% for those not using cell phones. Complete parts (a) and (b). a. Use the sample data to construct a 90% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system. D%The data below are yields for two different types of corn seed that were used on adjacent plots of land. Assume that the data are simple random samples and that the differences have a distribution that is approximately normal. Construct a 95% confidence interval estimate of the difference between type 1 and type 2 yields. What does the confidence interval suggest about farmer Joe's claim that type 1 seed is better than type 2 seed?Type 1 2143 2024 2142 2433 2142 2034 2211 1484 Type 2 2089 1924 2078 2467 2132 1949 2197 1482An economist is trying to determine the average per capita income (in thousands of dollars) of the residents of a major city in Texas. Suppose a sample of size 25 is drawn from the city with the following results: sample mean = 26 and sx = 9.6. Construct a 80% two-sided confidence interval for the mean per capita income. The Lower Limit of the two-sided confidence interval is: %3D O 23.4694 O 22.7149 O 22.0371 O 23.4733 O 22.7206 O 22.0448 O none of theseA study of 420,031 cell phone users found that 136 of them developed cancer of the brain or nervous system. Prior to this study of cell phone use, the rate of such cancer was found to be 0.0316% for those not using cell phones. Complete parts (a) and (b). a. Use the sample data to construct a 90% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system. %A. True or False? A researcher compares the BMI of two populations of individuals from different socioeconomic backgrounds and finds that the proportion of individuals considered obese and from a poor background is .37 (n = 112), and the proportion of individuals considered obese and from an affluent background is .27 (n = 87); a 95% confidence interval for the risk difference for obesity among members of the poor population compared to the affluent population is (-0.03, 0.23). B. Why is it true or false?Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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