A student is trying to decide whether on average rents for 1 1/2 apartments are
ID: 3205090 • Letter: A
Question
A student is trying to decide whether on average rents for 1 1/2 apartments are higher in Verdun than NDG. In the classified advertisments she finds 12 listings in Verdun with an average rent of 450$/month with standard deviation $50, in NDG 10 listings with average rent of $400 and standard deviation of $90. Suppose that the rents may be treated as normally distributed with the same variance in the two areas, and the listings represent random independent samples. Formulate the appropriate hypotheses and test at 10% level of significance. If actually the rents are higher on average in NDG than in Verdun, discuss the correctness of the answer in (a).Explanation / Answer
The null hypothesis would be :
Ho : Mean 1 = Mean 2
Ha : Both the means are different
Thus,
we perform t-test fro equality of means
P value and statistical significance:
The two-tailed P value equals 0.1149
By conventional criteria, this difference is considered to be not statistically significant.
Confidence interval:
The mean of Verdun minus NDG equals 50.00
95% confidence interval of this difference: From -13.28 to 113.28
Intermediate values used in calculations:
t = 1.6482
df = 20
standard error of difference = 30.337
The actual p-value obtained = 0.1149 which means that the null hypothesis can be rejected at 90% confidence level.
Hope this helps.
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