10 Probability and statistics attached

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10 Probability and statistics attached

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Question 1 Consider the following set of salary data: What assumptions are necessary to perform a test for the difference in population means? The two samples were independently selected from the populations of men and women. The population variances of salaries for men and women are equal. Both of the target populations have approximately normal distributions. All of these are necessary. Question 2 An inventor has developed a new spray coating that is designed to improve the wear of bicycle tires. To test the new coating, the inventor randomly selects one of the two tires on each of 50 bicycles to be coated with the new spray. The bicycle is then driven for 100 miles and the amount of the depth of the tread left on the two bicycle tires is measured (in millimeters). It is desired to determine whether the new spray coating improves the wear of the bicycle tires. The data and summary information is shown below: Use the summary data to construct a 90% confidence interval for the difference between the means. 0.53 ± 0.04512 0.53 ± 0.03787 0.53 ± 0.01396 0.53 ± 0.01663 Question 3 A confidence interval for (μ1 - μ2) is (5, 8). Which of the following inferences is correct? μ1 = μ2 μ1 < μ2 no significant difference between means μ1 > μ2 Question 4 We are interested in comparing the average supermarket prices of two leading colas. Our sample was taken by randomly selecting eight supermarkets and recording the price of a six-pack of each brand of cola at each supermarket. The data are shown in the following table: If the problem above represented a paired difference, what assumptions are needed for a confidence interval for the mean difference to be valid? The population variances are equal. The samples were independently selected from each population. The population of paired differences has an approximately normal distribution. All of these are needed. Question 5 Which of the following assumption is NOT necessary for two sample hypothesis t test (with two small size independent samples) to test population of true mean difference? The population means are equal. Both populations have approximately normal distributions. The samples were randomly and independently selected. Question 6 A marketing study was conducted to compare the mean age of male and female purchasers of a certain product. Random and independent samples were selected for both male and female purchasers of the product. It was desired to test to determine if the mean age of all female purchasers exceeds the mean age of all male purchasers. The sample data is shown here: Suppose the test statistic was calculated to be the value, t = 2.83. Make statistical decision when testing at level of significance alpha = 0.05 and determine degree of freedom. (Assume Welch's t test) We accept H0, degree of freedom =35 We reject H0, degree of freedom=38 We reject H0, degree of freedom =35 We fail to reject H0. Question 7 A certain manufacturer is interested in evaluating two alternative manufacturing plans consisting of different machine layouts. Because of union rules, hours of operation vary greatly for this particular manufacturer from one day to the next. Twenty-eight random working days were selected and each plan was monitored and the number of items produced each day was recorded. Some of the collected data is shown below: What assumptions are necessary for the above test to be valid? The population variances must be approximately equal. Both populations must be approximately normally distributed. The population of paired differences must be approximately normally distributed. None of these listed, since the Central Limit Theorem can be applied. Question 8 A paired difference experiment yielded nd pairs of observations. For the given case, what is the rejection region for testing H0: μd = 15 against Ha: μd < 15? nd = 21, α = 0.05 t < -1.721 t < -1.725 t < 2.086 t < 1.725 Question 9 Calculate the degrees of freedom associated with a small-sample test of hypothesis for assuming and 33 30 31 15 Question 10 A paired difference experiment yielded 27 pairs of observations. For the given case, what is the non-rejection region for testing H0: μD = 9 against Ha: μD > 9? α = 0.05 t > 1.706 t < 2.056 t > 2.056 t < 1.706
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