(a) A statistician wants to conduct a sample survey to estimate the population proportion of people who own a car. He plans to use the sample mean as an estimator. If he wants to have a margin of error not more than 3% at the 90% confidence level, what minimal sample size should be used? Answer: (b) The t-test for the null hypothesis Ho : / = Mo against the one-sided alternative Ha : u > Ho was applied and the Y value of the t-statistic t = 1.0 was obtained. On the following graph of the p.d.f. of the t-distribution with the appropriate number of degrees of freedom, show the area which corresponds to the p-value of this test. ..:... ..... : . . . ... .. . . .;.. . .;.. . . ........... . .. . . . . . . .. . . . . . .. ... . .;. ...... . .. . . . . .. . . ..:.. -2 (c) The 5% significance z-test for the null hypothesis Ho = 0 against the two-sided alternative hypothesis was applied to a sample of 16 elements obtained from a normal population with population standard deviation o = 2. Suppose that the actual population mean / = 1. On the graph below, sketch the p.d.f. of the z-statistic in this case and show the area under its graph which corresponds to the power of this test. . . . . :. .......... .. . ... . . . . .i . .... .. . ...;. . .. . . . . . . . . . .. . . .... . . . . :. ... .. . . . . ! . . .. .;.. . ... . .. . . . . .:. ... . . ........... . ! . . . ........ . . ... . ! . . .!. .. . . . . ... . .. .... . . . ... . . . . .. . . . . .... . . . . . ... . . . .. . . . . . . . . . ......... . . . . ... . . . .;. ... . . . ................ .. . . . .. . .. : . -. . . . . . ..!.. ................... .. .. . . ............"..... ................... . .......... . . . . .............. .S.. ........... . . . . . ...................... .. .... . . . . . . . ............ .... .............. . . . .. . . . . . . . .....'............. . . . .... . . .. . . . . .. .. . . . . . . . . . . . . .. .............. . . . .......... . ...! . . .....4............. . . . . . . . . . . . . .; . . ........... ... . .. ... ... ............. .. ... ...... ...... ............... . . . . . . -3 .. . . . . . . . . . .] . . . . . . . {. . .!.. . .!. . .'. . ? . . . .. . . . . .!.. .... . . . . .. . . . . . ... . . . . .. . Z A 5 -7 -6 -5 -4 -3 -2 -1 0 6

Answer rating: 100% (QA)

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