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- if variances are unequal, which would be an alternate non-parametric test for the independent samples t test?4. Find a 95% confidence interval for the difference of two means when you have independent samples, both of size 64, from two populations, in which the variances are not known to be equal. In this case, n₁-64, s₁²=6.1, the first sample mean is equal to 7.9; n2 =64, s2²-10.4, the second sample mean is equal to 8.5 Interpret the interval once you find it. Namely, can you conclude one mean is greater than the other mean and if so, which one?Define the bias of an arbitrary estimator and show that if an estimator is unbiased then the square error is equal to its variance.
- A company is doing a hypothesis test on the variation in quality from two suppliers. Both distributions are normal, and the populations are independent. Use a = 0.01. A sample of 22 products were selected from Supplier 1 and a standard deviation of quality was found to be 5.2696. A sample of 27 products were selected from Supplier 2 and a standard deviation of quality was found to be 3.8328. Test to see if the variance in quality for Supplier 1 is larger than Supplier 2. What are the correct hypotheses? Note this may view better in full screen mode. Select the correct symbols in the order they appear in the problem. Ho: Select an answer ? v Select an answer H1: Select an answer v Select an answer Based on the hypotheses, compute the following: Round answers to at least 4 decimal places. The test statistic is = The p-value is = The decision is to Select an answer v that the variance in The correct summary would be: Select an answer quality for Supplier 1 is larger than Supplier 2.A professor believes that the variance of ACT composite scores of honor students is less than that of all students who take the ACT. The sample variance of the ACT composite scores for a random sample of 15 honors students is 10.7. The sample variance of the ACT composite scores for a random sample of 18 other students is 24.2 Assume that both population distributions are approximately normal and test the professor’s claim using a 0.10 level of significance. Does the evidence support the professor’s claim? Let honor students be Population 1 and let students in general be Population 2. Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below. H0: σ21=σ22 Ha: σ21⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯σ22 Step 2 of 3: Compute the value of the test statistic. Round your answer to four decimal places. Step 3 of 3: Draw a conclusion and interpret the decision.A scientist wants to establish if the Mississippi’s river height has increased using data from 1970 and 2020. Historically, it’s known that the variance of the height within any given year is 4.5ft. The sample from 1970 has 80 measurements with ?1μ1 = 30ft and the sample from 2020 has 260 measurements with ?2μ2 = 31.5ft. Find a 95% confidence interval for the average increase of height.
- The Wilcoxon signed-rank test can be used to perform a hypothesis test for a population median, η, as well as for a population mean, μ. Why is that so?A light bulb manufacturer wants to compare the mean lifetimes of two of its light bulbs, model A and model B. Independent random samples of the two models were taken. Analysis of 13 bulbs of model A showed a mean lifetime of 1358 hours and a standard deviation of 105 hours. Analysis of 12 bulbs of model B showed a mean lifetime of 1357 hours and a standard deviation of 103 hours. Assume that the populations of lifetimes for each model are normally distributed and that the variances of these populations are equal. Construct a 90% confidence interval for the difference µ, –, between the mean lifetime lj of model A bulbs and the mean lifetime µ, of model B bulbs. Then find the lower limit and upper limit of the 90% confidence interval. Carry your intermediate computations to at least three decimal places. Round your responses to at least two decimal places. (If necessary, consult a list of formulas.) Lower limit:|| Upper limit:IA company is doing a hypothesis test on the variation in quality from two suppliers. Both distributions are normal, and the populations are independent. Use a = 0.01. A sample of 26 products were selected from Supplier 1 and a standard deviation of quality was found to be 6.0042. A sample of 25 products were selected from Supplier 2 and a standard deviation of quality was found to be 1.802. Test to see if the variance in quality for Supplier 1 is larger than Supplier 2. What are the correct hypotheses? Note this may view better in full screen mode. Select the correct symbols in the order they appear in the problem. Ho: Select an answer ✓ ? Select an answer H₁: Select an answer ? ✓ Select an answer Based on the hypotheses, compute the following: Round answers to at least 4 decimal places. The test statistic is = The p-value is The decision is to Select an answer The correct summary would be: Select an answer quality for Supplier 1 is larger than Supplier 2. ✓that the variance in
- The standard z-value of an arbitrary 16-unit sample from the normal-class population with a mean of 60 and a variance of 100 is 2.0.A professor claims that exam scores for non-accounting majors are more variable than for accounting majors. Random samples of 29 non-accounting majors and 29 accounting majors are taken from a final exam. Test at the 1% level the null hypothesis that the two population variances are equal against the alternative that the true variance is higher for the non-accounting majors. Assume the populations are normally distributed. Non-Accounting Accounting H₁:0² = 0² H₁:0² > 0² C. H₂:0² = 0² H₁:0² #0² nx = 29 ny = 29 S The critical value is X 2 represented by Ho and the alternative hypothesis is represented by H₁. Choose the correct answer below. OB. Ho: 0²20² H₁:0² <0² = 1611.016 = 446.238 2 OD. H₂:0² = 0² o H₁:0² <0² The test statistic is F = 3.610. (Round to three decimal places as needed.) (Round to two decimal places as needed.)Construct a 99% confidence interval for u, - H, with the sample statistics for mean cholesterol content of a hamburger from two fast food chains and confidence interval construction formula below. Assume the populations are approximately normal with unequal variances. Stats X1 = 105 mg, s, = 3.71 mg, n, = 16 X2 = 92 mg, s2 = 2.02 mg, n2 = 12 %3D si s3 Confidence interval when (X1 - X2) - to variances are not equalSEE MORE QUESTIONS
