The weights of a random sample of cereal boxes that are supposed to weigh 1 pound are given below. Estimate the standard deviation of the entire population with 92.8% confidence. 0.95 1.01 0.97 0.95 1.04 0.98 1.02 1.03
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- Use Excels functions (not @RISK) to generate 1000 random numbers from a normal distribution with mean 100 and standard deviation 10. Then freeze these random numbers. a. Calculate the mean and standard deviation of these random numbers. Are they approximately what you would expect? b. What fraction of these random numbers are within k standard deviations of the mean? Answer for k = 1; for k = 2; for k = 3. Are the answers close to what they should be (about 68% for k = 1, about 95% for k = 2, and over 99% for k = 3)? c. Create a histogram of the random numbers using about 10 bins of your choice. Does this histogram have approximately the shape you would expect?Federal Income Tax Returns. The Wall Street Journal reports that 33% of taxpayers with adjusted gross incomes between$30,000and$60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was$16,642. Assume the standard deviation is σ=$2400. What is the probability that a sample of taxpayers from this in-come group who have itemized deductions will show a sample mean within$200 of the population mean for sample sizes 30?Based on a random sample of size 75, you observe a sample mean of 85.63 and a sample standard deviation of 19.71. Which of the following are the endpoints of a 90% confidence interval for the population mean? (Because of potential roundoff, choose the closest.) a. 82.69 to 88.57 b. 81.84 to 89.42 c. 79.61 to 91.65 d. 81.10 to 90.16
- The Empirical Rule tells us that … a) __________ of the data lies within 1 standard deviation of the mean b) __________ of the data lies within 2 standard deviation of the mean c) __________ of the data lies within 3 standard deviation of the meanIn a school district, all sixth grade students take the same standardized test. The superintendant of the school district takes a random sample of 26 scores from all of the students who took the test. She sees that the mean score is 184 with a standard deviation of 18.2982. The superintendant wants to know if the standard deviation has changed this year. Previously, the population standard deviation was 17. Is there evidence that the standard deviation of test scores has increased at the α=0.01 level? Assume the population is normally distributed. Step 1 of 5 : State the null and alternative hypotheses. Round to four decimal places when necessary.The general meaning of a standard error is best described by which of the following? a. A standard error is another term for the estimated standard deviation of the population. b. If you go out about two standard errors on either side of 0, you can be about 95% confident that the unknown population parameter will be in the resulting interval. c. A standard error is essentially a standard deviation, specifically, the standard deviation of the sampling distribution of the estimate of the population parameter. d. All of these choices are correct characterizations of a typical standard error.
- The population’s mean is 30 and the mean of a sample of size 100 is 28.5. The variance of the sample is 25. The standard error of the sample mean is closest to: 0.05. 0.25. 0.50.In a random sample of 250 homeowners from a population of homeowners in a Florida resort community, 32 report that they had water damage during the past rainy season. The endpoints of a 95% confidence interval for the proportion of all homeowners who had water damage are closest to which of the following? a. 0.081 to 0.175 b. 0.073 to 0.182 c. 0.093 to 0.163 d. 0.087 to 0.169Small Mean Problem. Grandfather clocks have a particular market in auctions. You are given a random sample of 25 purchases of grandfather clocks at auctions in Pennsylvania. The sample statistics are: Mean = $1,343.04 Std Dev = $414.04 C.V. = 30.83 N = 25 You are asked to create a 95% Confidence Interval around the price for this sample. What is the Lower Bound for this confidence interval? I just want the answer. Use 2 decimal places for your answer and use the proper rules of rounding.
- A random survey of 250 homeowners in a resort community in Florida reported that water damage was reported in the last rainy season. The 95 percent trust intervals for the percentage of all homeowners with water loss are nearest to what? The above are 0.081 to 0.175 b. 0.073 to 0.182 C. 0.093 to 0.163 to 0.169 d. 0.087An industrial process that makes 3-foot sections of plasticpipe produces pipe with an average inside diameter of 1 inch and a standard deviation of .05 inch.a. If you randomly select one piece of pipe, what is the probability that its inside diameter willexceed 1.02 inches, assuming the population is normal?b. If you select a random sample of 25 pieces of pipe, what is the probability that the sample meanwill exceed 1.02 inches?μ = 1.00, σ = .05Each of these columns of data represent a different soda bottling line, with the values representing the amount of soda per bottle in ounces. The business question being asked for each of the three comparisons is "do the two bottling lines bottle the same volume of soda on average, bearing in mind that the sample difference that you may observe could just be coincidence." What is the null hypotheses? Alternative hypothesis P value Alpha=0.05 Is it significant ? t-Test: Two-Sample Assuming Unequal Variances C7 C8 Mean 20.01679499870 20.59290905613 Variance 0.01032479977 0.01011215081 Observations 50.00000000000 50.00000000000 Hypothesized Mean Difference 0.00000000000 df 98.00000000000 t Stat 28.49610006164 P(T<=t) one-tail 0.00000000000 t Critical one-tail 1.66055121707 P(T<=t) two-tail 0.00000000000 t Critical two-tail 1.98446745451