Question 934783: In the year 1990, a study was conducted that showed the average size of a newly constructed home in the U.S. was 2025 square feet. A researcher believes that in 2014 the average size of a newly constructed home is greater than it was in 1990. Suppose he takes a random sample of 100 newly constructed homes and finds the mean size of these homes is 2140 square feet with a standard deviation of 400 square feet. At a=0.05, is there enough evidence to support his claim?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 1990 average home = 2025 square feet.
sample of 100 in 2014 = 2140 square feet with standard deviation of 400 square feet.
one tailed study because the alternate assumption is that the average size of a newly constructed home is greater than it was in 1990.
the null assumption is that it is not greater.
sample size = n = 100
sample mean = 2140 in 2014
population mean = 2025 in 1990
sample standard deviation = 400
standard error = sample standard deviation divided by square root of sample size = 400 / sqrt(100) = 400 / 10 = 40
t-score is indicated because standard deviation is from sample and not from population.
t-score = (sample mean minus population mean) / standard error = (2140 - 2025) / 20 = 115 / 40 = 2.875
degrees of freedom equal sample size - 1 = 100 - 1 = 99
critical alpha = .05
1 - critical alpha = .95
critical t-score at .05 significance level with 99 degrees of freedom = ((.95,99) = 1.66
since the t-score is much greater than the critical t-score, there is no doubt that the average size of homes has increased and that the result of the sample is not just due to random variations in sample means of the same size from the same population.
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