1) One of the factors that a company will use in determining whether it will loc
ID: 3357445 • Letter: 1
Question
1) One of the factors that a company will use in determining whether it will locate a new facility in a community is the status of the real estate market. The managers believe the average length of time that homes stay on the market before selling They believe that if the mean time on the market is less than 45 days, the real estate market is favorable. To test this in a particular area, a random sample of n = 100 homes that sold during the past six months was selected. that an important measure of the real estate market is e mean for this sample was 40 days. It is believed that the population standard deviation is 15 days. If the test is conducted using a 0.05 level of significance, what conclusion should be reached? (15 marks)Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: > 45
Alternative hypothesis: < 45
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
SE = 1.5
DF = n - 1 = 100 - 1
D.F = 99
t = (x - ) / SE
t = - 3.33
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
Here is the logic of the analysis: Given the alternative hypothesis ( < 45), we want to know whether the observed sample mean is small enough to cause us to reject the null hypothesis.
The observed sample mean produced a t statistic test statistic of - 3.33.
Thus the P-value in this analysis is 0.000611.
Interpret results. Since the P-value (0.00061) is less than the significance level (0.05), we have to reject the null hypothesis.
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