Unbiasedness and the minimum mean squared error (MSE
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Distinguished carefully between the members of each of the following pairs of properties:
d. Unbiasedness and the minimum
e. Consistency and zero MSE.
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- To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, the Jacobs Chemical Company obtained the following data on the time (in minutes) needed to mix the material. Manufacturer 1 2 3 25 34 15 31 32 14 29 37 18 27 33 17 a. Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use a = 0.05. Sum of squares, treatment = Sum of squares, error = Mean squares, treatment = mean squares, error = Calculate the value of the test statistic (to 2 decimals). The P-value is: Less than 0.01, between 0.01 and 0.025, between 0.025 and 0.05, between 0.05 and 0.10, greater than 0.10 What is your conclusion? b. At the a = 0.05 level of significance, use Fisher's LSD procedure to test for the equality of the means for manufacturers 1 and 3. What conclusion can you draw after carrying out this test?The Management Department recently purchased a smallcopier for faculty use. Although the workload of the office staff has improved somewhat, the secretaries are still mak-ing too many trips to the Dean’s office when the depart-mental copier is out of service. Sylvia, the departmental secretary, has been keeping track of failure rates and ser-vice times. With a mean time between failures of 100 hours and a mean time to repair of 24 hours, how much of thetime is the new copier available for faculty use?Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again, and the net gain in grams is recorded. Using a significance level of 10%, test the hypothesis that the three formulas produce the same mean weight gain. (Let 1 = Linda's rats, 2 = Tuan's rats and 3 = Javier's rats.) Weights of Student Lab Rats Linda's rats Tuan's rats Javier's rats 43.0 46.9 51.1 38.5 40.1 40.4 40.7 38.4 37.1 45.8 45.7 44.8 37.8 43.6 47.7 Part (a) State the null hypothesis. H0: ?1 = ?2 = ?3 H0: At least two of the group means ?1, ?2, ?3 are not equal. Part (b) State the alternative hypothesis. Ha: ?1 = ?2 = ?3 Ha: At least two of the group means ?1, ?2, ?3 are not equal. Part (c) Enter an exact number as an…
- Compare the appropriate measures of center and variability for the two sets of data. Data Set A has a higher mean value of 8.8, and Data Set B has a lower range value of 8. Data Set A has a higher median value of 9, and Data Set B has a lower IQR value of 2.5. Data Set A has a lower mean value of 8.8, and Data Set B has a higher range value of 8. Data Set A has a lower median value of 9, and Data Set B has a higher IQR value of 8.Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 42 passengers, and a flight has fuel and baggage that allows for a total passenger load of 7,056 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 7,056 lb42=168 lb. What is the probability that the aircraft is overloaded? Should the pilot take any action to correct for an overloaded aircraft? Assume that weights of men are normally distributed with a mean of 178.3 lb and a standard deviation of 36.8.The mean output of solar cells of three types is measured six times under random light intensity over a period of 5 minutes, yielding the results shown. Research question: Is the mean solar cell output the same for all cell types?
- A cruise ship charges passengers $3 for a can of soda. Because of passenger complaints, the ship manager has decided to try out a plan with a lower price. He thinks that with a lower price, more cans will be sold, which would mean that the ship would still make a reasonable total profit. With the old pricing, the mean number of cans sold per passenger for a 10-day trip was 10.3 cans. Suppose μ represents the mean number of cans per passenger for the new pricing. What hypotheses should the ship manager test if he wants to determine if the mean number of cans sold is greater for the new pricing plan? O Ho: μ = 10.3 versus H₂: μ> 10.3 O Ho: μ = O Ho: μ = 10 versus Ha: μ 10.3f.To study how well rats can learn, behavioral scientists used a sample of rats in a maze experiment. Each rat had to find itway through a maze to reach a treat at the end. The rat was timed on its first trial run and again on its tenth eighth trial run. The difference in the times was recorded for each rat. Which of the following is the most appropriate procedure for the scientists to use? A- A matched pair t-interval for a mean diffderence B- A two sample t interval for a difference between means C- a one sample t interval for a sample difference D-A one sample z interval for a population proportion E- A two sample z interval for a difference between proportions
- undergraduate students taking a concepts and methods course at the university conducted a survey about GPA and major. There were 197 total students and 3 groups of majors that were randomly sampled. The mean square within groups was 0.081 and the mean square between groups was 0.015. What F-statistic output is correct for this problem?Calculate inter-quartile range and its co-efficient from the following data: Wages ( $ ) 15 25 35 45 55 No. of Workers : 6 14 22 12Which of the following is the research hypothesis of one-tailed dependent t-test expecting to see a significant decrease in the observed scores? A. mean(posttest) < mean(pretest) B. mean(posttest) = mean(pretest) C. mean(posttest) > mean(pretest) D. mean(posttest) ≠ mean(pretest)