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- Chapter 6, Section 4-HT, Exercise 212 Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distributions are relatively normal.Test H0 : μT=μC vs Ha : μT<μC using the fact that the treatment group (T) has a sample mean of 8.6 with a standard deviation of 4.1 while the control group (C) has a sample mean of 11.2with a standard deviation of 3.4. Both groups have 25 cases. (a) Give the test statistic and the p-value.Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places.test statistic = p-value = (b) What is the conclusion of the test at a 5% significance level? Reject H0. Do not reject H0.The 30 management professors at Omega University find out that telephone calls made to their offices are not being picked up. A call-forwarding system redirects calls to the management office after the fourth ring. A department office assistant answers the telephone and takes messages.An average of 90 telephone calls per hour is placed to the management faculty, and each telephone call consumes about one minute of the assistant’s time. The calls arrive to a Poisson distribution, as shown in Figure (a), with an average of 1.5 calls per minute. Because the professors spend much of their time in class and in conferences, there is only a 40 percent chance that they will pick up a call themselves, as shown in Figure (b). If two or more telephone calls are forwarded to the office during the same minute, only the first call will be answered.a. Without using simulation, make a preliminary guess of what proportion of the time the assistant will be on the telephone and what proportion of the…Consider a capital market with only two risky assets A and B. Their standard deviations are 1 and 2, respectively. There is no risk-free asset. When the correlation coefficient ρAB = 0, construct a portfolio, whose variance is strictly less than 1. [Hint: you may want to try the portfolio that puts more weight on the security with the lower standard deviation.]
- What is the difference between heteroskedasticity and homoskedasticityChapter 6, Section 5, Exercise 236 Use a t-distribution and the given matched pair sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distribution of the differences is relatively normal. Assume that differences are computed using d=x1-x2.Test H0 : μd=0 vs Ha : μd≠0 using the paired difference sample results x¯d=10.51, sd=11.6, nd=25. Give the test statistic and the p-value.Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places.test statistic = Enter your answer; test statisticp-value = Enter your answer; p-value Give the conclusion using a 5% significance level. Reject H0. Do not reject H0.Chapter 6, Section 4-HT, Exercise 211 Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distributions are relatively normal.Test H0 : μA=μB vs Ha : μA≠μB using the fact that Group A has 8 cases with a mean of 125 and a standard deviation of 18 while Group B has 15 cases with a mean of 118 and a standard deviation of 14. (a) Give the test statistic and the p-value.Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places.test statistic = Enter your answer in accordance to item (a) of the question statementp-value = Enter your answer in accordance to item (a) of the question statement (b) What is the conclusion of the test? Test at a 10% level. Reject H0.…
- In a Denver community, 50 cases of diabetes were reported among 15-19 years old out of a total population of 46,000 between September 1 to December 31, 2016. Ten percent (4,600) of the population were between 15-19 years old on April 1, 2016 and the size and age distribution of the population has remained constant. An investigation of the cases in the 15-19-year age group revealed that 22 of the reported cases were contracted prior to September 1. In addition, another 18 cases developed in April and May but were clinically resolved before September 1. What was the cumulative incidence rate of disease in 15-19 year olds per 1,000 population in this Denver community during the period September 1 to December 31, 2016?1. The sample mean weights for two varieties of lettuce grown for 16 days in a controlled environment are 3.259 and 1.413 and the corresponding sample standard deviations are .400 and .220. If the sample sizes for the two varieties are 9 and 6 respectively, what would be the pair of hypotheses to test if the two varieties of lettuce have the same average weight? (Given: weight of each variety of lettuce is normally distributed). A. H0: μ1 ≠ μ2 vs H1: μ1 = μ2 B. H0: μ1 = μ2 vs H1: μ1 ≠ μ2 C. H0: μ1 > μ2 vs H1: μ1 ≤ μ2 D. H0: μ1 ≤ μ2 vs H1: μ1 > μ2 2. At 5% level, what are the critical values for testing equality of mean weights in problem 1? A. 2.18 B. -2.18 and 2.18 C. -1.78 D.-1.78 and 1.78 3.What is the best decision using critical value approach in problem 1? A. The computed test statistic falls in the critical region and we do not reject the null hypothesis. B. The computed test statistic does not fall in the critical…1. The sample mean weights for two varieties of lettuce grown for 16 days in a controlled environment are 3.259 and 1.413 and the corresponding sample standard deviations are .400 and .220. If the sample sizes for the two varieties are 9 and 6 respectively, what would be the pair of hypotheses to test if the two varieties of lettuce have the same average weight? (Given: weight of each variety of lettuce is normally distributed). A. H0: μ1 ≠ μ2 vs H1: μ1 = μ2 B. H0: μ1 = μ2 vs H1: μ1 ≠ μ2 C. H0: μ1 > μ2 vs H1: μ1 ≤ μ2 D. H0: μ1 ≤ μ2 vs H1: μ1 > μ2 2.What would be the degree of freedom for the test statistic in problem 1? A. 6 B. 9 C. 12.7 D. 14 3. What would be the computed test statistic in problem 1? A. 2.93 B. 3.57 C. 8.44 D. 11.48
- 1. The sample mean weights for two varieties of lettuce grown for 16 days in a controlled environment are 3.259 and 1.413 and the corresponding sample standard deviations are .400 and .220. If the sample sizes for the two varieties are 9 and 6 respectively, what would be the pair of hypotheses to test if the two varieties of lettuce have the same average weight? (Given: weight of each variety of lettuce is normally distributed). A. H0: μ1 ≠ μ2 vs H1: μ1 = μ2 B. H0: μ1 = μ2 vs H1: μ1 ≠ μ2 C. H0: μ1 > μ2 vs H1: μ1 ≤ μ2 D. H0: μ1 ≤ μ2 vs H1: μ1 > μ2 2. What is the best decision using critical value approach in problem 1? A. The computed test statistic falls in the critical region and we do not reject the null hypothesis. B. The computed test statistic does not fall in the critical region and we do not reject the null hypothesis. C. The computed test statistic falls in the critical region and we reject the null hypothesis. D.The computed…1. The sample mean weights for two varieties of lettuce grown for 16 days in a controlled environment are 3.259 and 1.413 and the corresponding sample standard deviations are .400 and .220. If the sample sizes for the two varieties are 9 and 6 respectively, what would be the pair of hypotheses to test if the two varieties of lettuce have the same average weight? (Given: weight of each variety of lettuce is normally distributed). A. H0: μ1 ≠ μ2 vs H1: μ1 = μ2 B. H0: μ1 = μ2 vs H1: μ1 ≠ μ2 C.H0: μ1 > μ2 vs H1: μ1 ≤ μ2 D. H0: μ1 ≤ μ2 vs H1: μ1 > μ2 2. What is the best decision using critical value approach in problem 1? A. The computed test statistic falls in the critical region and we do not reject the null hypothesis. B. The computed test statistic does not fall in the critical region and we do not reject the null hypothesis. C. The computed test statistic falls in the critical region and we reject the null hypothesis. D. The computed test statistic does not fall…A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 425 gram setting. Is there sufficient evidence at the 0.01 level that the bags are underfilled or overfilled? Assume the population is normally distributed. State the null and alternative hypotheses for the above scenario.
