Faculty of Humanities and Social Sciences - Social Science Assignment Help

Assignment Task

Task

01. For a population of size N=5 the values of the variable X are 8, 4, 12, 10, 6.
i. Calculate the sample mean for all possible simple random samples of size 2 from the population.
ii. Verify that the sample mean is an unbiased estimator for the population mean.
iii. Calculate the variance of using the sampling distribution.
02. Two types of insulation are applied to houses and then the temperatures are measured at midnight for each house. The temperatures yielded from both methods are normally distributed with the same variance. The first method was applied to 15 houses, yielding a mean temperature of 3.7 and variance 2.8; the second method was also applied to 15 other houses, yielding a mean temperature
of 4.75 and variance 0.18. Do hypothesis testing to confirm or reject that the two methods yield the same population mean at 5% significance level.
03. Two types of insulation are applied to houses and then the temperatures are measured at midnight for each house. The first method was applied to 30 houses, yielding a mean temperature of 3.7 and variance 2.8; the second method was also applied to 30 other houses, yielding a mean temperature of 4.75 and variance 0.18. Do hypothesis testing to confirm or reject that the two methods yield the same population mean at ? = 0.05.
 

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