(iv) A geneticist is interested in measuring the true mean number of mutations (u) per culture that occur in E.Coli bacteria when cultivated in the presence of Dioxin. Suppose the overall standard deviation of the number of mutations is 22. What is the approximate sampling distribution of the sample mean number of mutations for a random sample of n=100 cultures of bacteria? b. Normal(u, 22/100) a. Normal(u, 22²/100 ) d. Normal(u, 22) c. Normal(u, 222)
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- Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributedpopulations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts. Diet Regular μ μ1 μ2 n 33 33 x 0.78488 lb 0.80356 lb s 0.00444 lb 0.00744 lb a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. i) What are the null alternative hypothesis? ii) What's the test statics? iii) What's the P-value? iv) State the conclusion vi) construct a confidence interval suitable suitable for testing the claim that the two samples are from populations with the same mean vii) Does the confidence interval…(5). Calculate SS, variance and standard deviation for the following sample of n=7 scores: 8, 6, 5, 2, 6, 3, 5.2) In the population, IQ scores are normally distributed with a mean of 100 and standard deviation of 15. We repeatedly pulled random samples of 50 individuals from the population and measured their IQ and the resulted mean was 92 with a standard deviation of 8. Test at a =0.05 significance if there is any statistically significant difference in the variance of the result. D. Focus DELL
- Gestation Periods of Humans. For humans, gestation periods are normally distributed with a mean of 266 days and a standard deviation of 16 days. Suppose that you observe the gestation periods for a sample of nine humans. a. Theoretically, what are the mean and standard deviation of all possible sample means? b. Use the technology of your choice to simulate 2000 samples of nine human gestation periods each. c. Determine the mean of each of the 2000 samples you obtained in part (b). d. Roughly what would you expect the mean and standard deviation of the 2000 sample means you obtained in part (c) to be? Explain your answers. e. Determine the mean and standard deviation of the 2000 sample means you obtained in part (c). f. Compare your answers in parts (d) and (e). Why are they different?Data on the weights (Ib) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts. Diet Regular H2 27 27 0.79037 lb 0.80399 lb 0.00449 lb 0.00756 lb a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? O A. Ho: H1 = H2 OB. Ho: H1#H2 Hq: Hy4. A normal population has the mean of 20 and the variance of 100. A random sample of size n = 69 is selected. (a) Find the standard deviation of the sample mean. (b) How large must the sample be if you want to halve the standard deviation of the sample mean?D A small amount of the trace element selenium, 50-200 micrograms (ug) per day, is considered essential to good health. Suppose that random samples of 50 adults were selected from two regions of the United States and that each person's daily selenium intake was recorded. The means and standard deviations of the selenium daily intakes for the two groups are shown in the table. Sample Mean (ug) Sample Standard Deviation (ug) Find a 95% confidence interval for the difference (₁-₂) in the mean selenium intakes for the two regions. (Round your answers to three decimal places.) 49 Region Phase One-Tw_docx 1 167.4 22.8 ug to Interpret this interval, O The probability that the difference in the average daily selenium intake for the populations in Region 1 and Region 2 is exactly in the middle of the Interval is 95%. A 2 140.5 17.3 O The probability that the difference in the average daily selenium intake for the populations in Region 1 and Region 2 is within the interval is 95%. We are 95%…Let X 1 , … , X n be identically and independently distributed with population mean 9.3 and standard deviation 1.400. Let xbar be the sample mean, xbar = 1 n ∑ i = 1 n X i. Suppose n = 14. What is the mean squared error (MSE) of 0.742*xbar as an estimator for the population mean?Data on the weights (Ib) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. Diet Regular H2 nts 34 0.80711 lb 34 0.79119 lb 0.00432 lb 0.00747 lb 車 ent a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? bra O B. Ho H1 H2 Hq: Hy < H2 O A. Ho: H1 = H2 on! O D. Hg: H1 = H2 O C. Ho H H2 The test statistic, t, is (Round to two decimal places as needed.) The P-value is |. (Round to three decimal places as needed.) State the conclusion for the test. n oonr of diet soda have mean weights that are lower than the mean weightIf the z-value for a given x of a random variable Z is z =1.06, and the distribution of X is normal with a mean of 60 and a standard deviation of 6, to what x-value does this z-value correspond?Data on the weights (Ib) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts. Diet Regular H2 26 26 0.79911 Ib 0.81326 Ib S 0.00445 Ib 0.00759 Ib ..... a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? A. Ho: Hy =H2 H1: 41> H2 B. Ho: H1 = H2 H1: 41Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. 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