A light bulb manufacturer wants to compare the
Carry your intermediate computations to at least three decimal places. Round your responses to at least two decimal places.
Upper Limit
Lower Limit:
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- The university data center has two main computers. The center wants to examine whether computer 1 is receiving tasks that require processing times comparable to those of computer 2. A random sample of 12 processing times from computer 1 showed a mean of 67 seconds with a standard deviation of 20 seconds, while a random sample of 11 processing times from computer 2 (chosen independently of those for computer 1) showed a mean of 70 seconds with a standard deviation of 16 seconds. Assume that the populations of processing times are normally distributed for each of the two computers and that the variances are equal. Construct a 90% confidence interval for the difference u, -4, between the mean processing time of computer 1, µ,, and the mean processing time of computer 2, µ„. 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,…arrow_forwardThe variability in the amounts of impurities present in a batch of chemical used for a particular process depends on the length of time the process is in operation. A manufacturer using two production lines, 1 and 2, has made a slight adjustment to line 2, hoping to reduce the variability as well as the average amount of impurities in the chemical. Samples of 25 and 25 measurements from the two batches yield 1.04, respectively 0.51 variances. Do the data present sufficient evidence to indicate that the process variability is less for line 2? Use 5% significance level. Conduct a hypothesis test of the airline executive’s belief. [α = 0.05]arrow_forwardIt is hypothesized that the total sales of a corporation should vary more in an industry with active price competition than in one with duopoly and tacit collusion. In a study of the merchant ship production industry it was found that in 4 years of active price competition, the variance of company A’s total sales was 114.09. In the following 7 years, during which there was duopoly and tacit collusion, this variance was 16.08. Assume that the data can be regarded as an independent random sample from two normal distributions. 1. Test, at the 5% level, the null hypothesis that the two population variances are equal against the alternative that they are not equal.arrow_forward
- One study claims that the variance in the resting heart rates of smokers is different than the variance in the resting heart rates of nonsmokers. A medical student decides to test this claim. The sample variance of resting heart rates, measured in beats per minute, for a random sample of 9 smokers is 480.7. The sample variance for a random sample of 9 nonsmokers is 131.6. Assume that both population distributions are approximately normal and test the study’s claim using a 0.10 level of significance. Does the evidence support the study’s claim? Let smokers be Population 1 and let nonsmokers 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.arrow_forwardchester butchery supplies vienna sausages in the entire kzn province. a meat packer is investigating the marked mass shown on vienna sausages. a pilot study showed a mean of 11.8kg per pack and a variance of 0.49kg. how many packs should be sampled in order to be 92% confident that the sample mean will differ by at most 0.2kg.arrow_forwardThe university data center has two main computers. The center wants to examine whether computer 1 is receiving tasks that require processing times comparable to those of computer 2 . A random sample of 14 processing times from computer 1 showed a mean of 54 seconds with a standard deviation of 20 seconds, while a random sample of 9 processing times from computer 2 (chosen independently of those for computer 1 ) showed a mean of 61 seconds with a standard deviation of 19 seconds. Assume that the populations of processing times are normally distributed for each of the two computers and that the variances are equal. Construct a 95% confidence interval for the difference −μ1μ2 between the mean processing time of computer 1 , μ1 , and the mean processing time of computer 2 , μ2 . Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your responses to at least two decimal places. (If necessary, consult a…arrow_forward
- A researcher decides to measure anxiety in group of bullies and a group of bystanders using a 23-item, 3 point anxiety scale. Assume scores on the anxiety scales are normally distributed and the variance among the group of bullies and bystanders are the same. A group of 30 bullies scores an average of 21.5 with a sample standard deviation of 10 on the anxiety scale. A group of 27 bystanders scored an average of 25.8 with a sample standard deviation of 8 on the anxiety scale. You do not have any presupposed assumptions whether bullies or bystanders will be more anxious so you formulate the null and alternative hypothesis based on that.arrow_forwardThe university data center has two main computers. The center wants to examine whether computer 1 is receiving tasks which require comparable processing time to those of computer 2. A random sample of 11 processing times from computer 1 showed a mean of 35 seconds with a standard deviation of 20 seconds, while a random sample of 7 processing times from computer 2 (chosen independently of those for computer 1) showed a mean of 58 seconds with a standard deviation of 18 seconds. Assume that the populations of processing times are normally distributed for each of the two computers, and that the variances are equal. Can we conclude, at the 0.1 level of significance, that the mean processing time of computer 1, μ1, differs from the mean processing time of computer 2, μ2?Perform a two-tailed test. 1.The null hypothesis: 2.The alternative hypothesis: 3.The value of the test statistic:(Round to at least three decimal places.) 4.The p-value:(Round to at least three decimal places.)arrow_forwardThe university data center has two main computers. The center wants to examine whether computer 1 is receiving tasks which require comparable processing time to those of computer 2. A random sample of 9 processing times from computer 1 showed a mean of 78 seconds with a standard deviation of 17 seconds, while a random sample of 12 processing times from computer 2 (chosen independently of those for computer 1) showed a mean of 65 seconds with a standard deviation of 16 seconds. Assume that the populations of processing times are normally distributed for each of the two computers, and that the variances are equal. Can we conclude, at the 0.10 level of significance, that the mean processing time of computer 1, μ1, is greater than the mean processing time of computer 2, μ2? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. a. State the null hypothesis H0 and the…arrow_forward
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