A sample of certain observations selected from a normally distributed population produced a sample variance of 38. Construct a 98% confidence interval for the population variance for each of the following cases and comment on the intervals as the sample size increases. (а) п — 12 (b) п — = 16 (с) п — 20 (а) п — 12
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- 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. 11.481. 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…1. The average weight of a group of individuals in a weight loss program was originally 200 pounds. After 2 weeks of the program, a sample of 60 such individuals are considered, and it is found that the average weight for these sampled individuals is 180 pounds with a standard deviation of 80 pounds. What would be the pair of hypotheses to test if the average weight has gone down. A. H0 : μ ≥ 200 vs Ha : μ < 200 B. H0 : μ > 200 vs Ha : μ < 200 C. H0 : μ <200 vs Ha : μ > 200 D. H0 : μ < 200 vs Ha : μ ≥ 200 2. If the level of significance is given to be 5%, what would be your decision using the p-value approach? A. The p value is less than or equal to 0.05 and we fail to reject the null hypothesis B. The p value is less than or equal to 0.05 and we reject the null hypothesis C. The p value is greater than 0.05 and we reject the null hypothesis D. The p value is greater than 0.05 and we fail to reject the null hypothesis 3.…1. The average weight of a group of individuals in a weight loss program was originally 200 pounds. After 2 weeks of the program, a sample of 60 such individuals are considered, and it is found that the average weight for these sampled individuals is 180 pounds with a standard deviation of 80 pounds. What would be the pair of hypotheses to test if the average weight has gone down. A. H0 : μ ≥ 200 vs Ha : μ < 200 B. H0 : μ > 200 vs Ha : μ < 200 C. H0 : μ <200 vs Ha : μ > 200 D. H0 : μ < 200 vs Ha : μ ≥ 200 2.What would be the standard error of the sample mean in problem 1? A. 1.15 B. 1.33 C. 10.33 D. 12 3. What would be the p-value for testing the pair of hypotheses in problem 1? A. 0.1 B. 0.058 C. 0.05 D. 0.029
- A researcher selects a sample from a population with a mean of m = 40 and administers a treatment to the individuals in the sample. If the treatment is expected to decrease scores, which of the following is the correct statement of the null hypothesis for a one-tailed test? ��� a. The researcher must fail to reject the null hypothesis with either α = .05 or α = .01. b. The researcher can reject the null hypothesis with either α = .05 or α = .01. c. The researcher can reject the null hypothesis with α = .05 but not with α = .01. d. It is impossible to make a decision about H0 without more information.An engineer is comparing voltages for two types of batteries (K and Q) using a sample of 7070 type K batteries and a sample of 8585 type Q batteries. The type K batteries have a mean voltage of 8.848.84, and the population standard deviation is known to be 0.3030.303. The type Q batteries have a mean voltage of 9.059.05, and the population standard deviation is known to be 0.3670.367. Conduct a hypothesis test for the conjecture that the mean voltage for these two types of batteries is different. Let μ1μ1 be the true mean voltage for type K batteries and μ2μ2 be the true mean voltage for type Q batteries. Use a 0.010.01 level of significance. Step 1 of 4 : State the null and alternative hypotheses for the test.An engineer is comparing voltages for two types of batteries (K and Q) using a sample of 7070 type K batteries and a sample of 8585 type Q batteries. The type K batteries have a mean voltage of 8.848.84, and the population standard deviation is known to be 0.3030.303. The type Q batteries have a mean voltage of 9.059.05, and the population standard deviation is known to be 0.3670.367. Conduct a hypothesis test for the conjecture that the mean voltage for these two types of batteries is different. Let μ1μ1 be the true mean voltage for type K batteries and μ2μ2 be the true mean voltage for type Q batteries. Use a 0.010.01 level of significance. Step 3 of 4 : Determine the decision rule for rejecting the null hypothesis H0H0. Round the numerical portion of your answer to three decimal places.
- A district official intends to use the mean of a random sample of 900 sixth graders from a very large school district to estimate the mean score that all the sixth graders in the district would get if they took a certain arithmetic achievement test. The official knows that σ=9.4 for such data. Suppose that the district official takes her sample and gets x=61.8. Use the above variance formula to construct a 99% confidence interval for the mean score of all the sixth graders in the district.1. A pollster wants to conduct a pre-election poll with a margin of error of 3.5% and a 95% confidence level. The pollster does not know ahead of time what the proportion in favor of either candidate is. How many people must be included in the sample to achieve the goal of a 3.5% margin of error? [Note that p -hat is unknown and is therefore assumed to be 0.5.] 2. In another pre-election poll, a pollster finds that 438 out of 600 people polled favor, Smith. Construct the 95% confidence interval for the proportion (to nearest 0.001) of people in the whole population who favor Smith.A researcher obtains a correlation of r = 0.40 for a sample of n = 25 individuals. If we use a two-tailed test Which of the following is the correct statistical decision a.Reject the null hypothesis with an alpha level of .05 b.Reject the null hypothesis with an alpha level of .01 c.Fail to reject the null hypothesis with an alpha level of .05 d.There is not enough information to make a statistical decision