The mean of several thousand apartments in a new development is advertised to be 1250 square feet (w
Statistics

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The mean of several thousand apartments in a new development is advertised to be 1250
square feet (with a standard deviation of 38 sq. ft.). A tenant group thinks that the apartments are smaller
than advertised after taking a sample of 150 apartments and finding the average square footage to be only
1245. Does the tenant group have significant evidence (alpha = .01) that the new development is using
false advertisement?
I believe that the tenant group does not have significant evidence that the new development is using false advertisement.
we will fail to reject Ho in favor of μ = 1250 on apt squarefootage .
Null hypothesis is
Ho : μ = 1250 μ = squarefootage of apt.
Alternative hypothesis
Ha : μ < 1250 squarefoot where μ is the mean area of apartments
Population is several thousand apartment
variable = square footage
Parameter μ =1250 squarefoot
Null hypothesis is
Ho : μ = 1250 μ = squarefootage of apt.
alternative hypothesis is
Ho : μ < 1250 μ
Using a 90% confidence level margin of error is 10 squarefeet
10 = 1.645(38/squarerroot n) = 40 OR
n = (1.645 *38/10)^2 = 40(39.07)
test statistic zscore
zscore = 12451250/ 38/ square root 150 = 1.61
P( z) = .05
we will fail to reject Ho in favor of μ = 1250 on apt squarefootage .
If the relationship between the two variables is strong (as assessed by a Measure of Association), and the level chosen for alpha is .05, then moderate or small sample sizes will detect it.
As relationships get weaker, however, and/or as the level of alpha gets smaller, larger sample sizes will be needed for the research to reach statistical significance.
Here the sample size is 150 and alpha =.01
If the relationship between the two variables is strong (as assessed by a Measure of Association), and the level chosen for alpha is .05, then moderate or small sample sizes will detect it.
Researchers generally specify the probability of committing a Type I error that they are willing to accept, i.e., the value of alpha.
https://web.csulb.edu/~msaintg/ppa696/696sts
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