Construct and interpret a 90% confidence interval for the population mean µ.
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Q: Construct the confidence interval for the population mean.
A: Answer:
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Q: What is the sample standard deviation?
A: To Discuss: What is the sample standard deviation?
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A: Solution: Let X be the random variable. From the given information, x-bar=30, s=3.5 and n=15.
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- 1. The following table illustrates the BMI for a number of patients recently enrolled in a study investigating the relationship between BMI and type 2 diabetes. Participant BMI (kg/m2) A 26.5 B 19.2 C 29.7 D 27.4 E 30.2 F 28.9 A) Assuming the participants can be considered to be normally distributed, and that they comefrom a population with a σ=2.4 kg/m2, calculate a 95% confidence interval for the mean BMI ofthe population for which they represent.B) Correctly interpret the confidence interval you found above.A 30 month study is conducted to determine the difference in rates of accidents per month between two departments in an assembly plant. If a sample of 12 from the first department averaged 12.3 accidents per month with a standard deviation of 3.5, and a sample of 9 from the second department averaged 7.6 accidents per month with standard deviation of 3.4, find: The t-value for a 95% confidence interval is: A. 2.09302 B. 1.724718 C. 2.08596 D. 1.729133 E. none of the preceding: A sample of 8 earnings per share estimates for 1998 is shown below: AT&T 2.92 Caterpillar 4.65 Eastman Kodak 4.27 Exxon 3.09 Hewlett-Packard 3.57 IBM 7.04 McDonald’s 2.64 Wal-Mart 1.74 Compute the sample variance and sample standard deviation for these data? 2. What is the 95% confidence interval for the population variance? 3. What is the 95% confidence interval for the population standard deviation?
- R&D department believes that the C-type batteries with a nominal diameter of 2mm will fit properly into all toys. A tolerance variation of 0.000225mm2 is allowable. A machine produces a batch of 12 C-type batteries and the following diameters in mm is recorded. 26.22 26.19 26.24 26.21 26.16 26.18 26.21 26.20 26.22 26.19 26.20 26.18 i) Construct a 95% confidence interval for the population ii) Does this variation appear acceptable?The following table illustrates the BMI for a number of patients recently enrolled in a study investigating the relationship between BMI and type 2 diabetes. Participant BMI (kg/m2) A 26.5 B 19.2 C 29.7 D 27.4 E 30.2 F 28.9 A) Assuming the participants can be considered to be normally distributed, and that they come from a population with a σ=2.4 kg/m , calculate a 95% confidence interval for the mean BMI of the population for which they represent and correctly interpret the confidence interval you found.What price do farmers get for their seedless watermelon crops? In a recent month, a simple random sample of 31 farming regions gave a sample mean of $12.15 per 100 pounds of seedless watermelon. Assumer that σ=$1.46 per 100 pounds. Find the sample size necessary for a 90% confidence level with a margin of error E=0.61 for the mean price per 100 pounds of seedless watermelon. (Increase to the next whole number.)
- A group of six individuals with high cholesterol levels were given a new diet designed to lower cholesterol levels. Cholesterol levels, in milligrams per deciliter, were measured before and after the implementation of the diet for each individual, with the following results: Before After 227 160 234 174 257 178 269 170 218 178 248 178 A dietician claims that the mean reduction in cholesterol level is 51 milligrams per deciliter. Find the 98% confidence interval for the mean reduction in cholesterol level. Interpret the results. Does the 98% confidence interval contradict this claim?A researcher estimates the 90% CI for a sample with a mean of M = 8.9 and a standard error (sM) of 2.1. What is the confidence interval at this level of confidence?