Round all intermediate calculations to at least 4 decimal places.) An entreprene
ID: 3055515 • Letter: R
Question
Round all intermediate calculations to at least 4 decimal places.) An entrepreneur owns some land that he wishes to develop. He identifies two development options: build condominiums or build apartment buildings. Accordingly, he reviews public records and derives the following summary measures concerning annual profitability based on a random sample of 32 for each such local business venture. For the analysis, he uses a historical (population) standard deviation of $21,900 for condominiums and $19,900 for apartment buildings. Use Table 1 Sample 1 represents condominiums and Sample 2 represents apartment buildings Condominiums 1 $249,000 n1 32 Apartment Buildings 2 $235,200 n2 32 a. Set up the hypotheses to test whether the mean profitability differs between condominiums and apartment buildings b. Compute the value of the test statistic and the corresponding p-value. (Round "test statistic" value to 2 decimal places and "p-value" to 3 decimal places.) Test statistic p-value c-1. At the 10% significance level, what is the conclusion to the test? H-At either the 10% significance levels, we cannot conclude the Reject mean profitability differs between condominiums and apartment buildings C-2. At the 1% significance level, what is the conclusion to the test? conclude the Ho. At either the 1% significance levels, we can mean profitability differs between condominiums and apartment buildings Do not rejectExplanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: u1 = u 2
Alternative hypothesis: u1 ? u 2
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.10. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 5230.9774
DF = 62.0
t = [ (x1 - x2) - d ] / SE
t = 2.64
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.
Since we have a two-tailed test, the P-value is the probability that a t statistic having 62 degrees of freedom is more extreme than -2.64; that is, less than -2.64 or greater than 2.64.
Thus, the P-value = 0.01.
Interpret results. Since the P-value (0.01) is less than the significance level (0.10), we have to reject the null hypothesis.
Reject H0, At either the 10% significance levels, we can conclude the mean profitability differs between condominiums and apartment buildings.
From the above test we have sufficient evidence in the favor of the claim that there is significance
Thus, the P-value = 0.01.
Interpret results. Since the P-value (0.01) is greater than the significance level (0.01), we have to accept the null hypothesis.
Do not reject H0. At either the 1% significance levels, we cannot conclude the mean profitability differs between condominiums and apartment buildings.
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