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

label 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?

Apr 14th, 2015

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 z-score

z-score = 1245-1250/ 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


Apr 14th, 2015

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