Underlying Standard Deviation System †Free Samples to Students

Question: Discuss about the Underlying Standard Deviation System. Answer: Introduction: The suburb 1 has been taken as New Town while the suburb 2 has been taken as Hurstville. A sample data of 50 samples for the weekly rent has been collected for both the suburbs (Source: https://www.realestate.com.au/buy ). The population of interest in each case would be all the rented apartments which are located in the respective suburbs. From this population, for the given task, 50 samples have been randomly selected. Hypothesis Testing Rent in New Town The objective is to determine on the basis of the collected sample management as to whether the average weekly rent in New Town is greater than $ 450 or not. Since inference about the population has to be drawn using sample, hence inferential statistics would be deployed. The relevant hypotheses for the given test are indicated below. Null Hypothesis (Ho): $450 i.e. the weekly rent of apartment in New Town is less than or equal to $ 450 Alternate Hypothesis (H1): $450 i.e. the weekly rent of apartment in New Town is more than $ 450 It is apparent that the given hypothesis test would be a right tail test. Also, since the standard deviation of the weekly rent of the population is not known, hence the appropriate test statistic to be used would be t and not z. Sample mean = $ 661.7 Sample standard deviation = $ 300.99 Sample size = 50 Hence, standard error = 300.99/50 = 42.57 Thus, t statistics = (661.7-450)/42.57 = 4.97 Degrees of freedom = 50-1 = 49 For the above degree of freedom and t stat = 4.97, the corresponding p value comes out as 0.00. Assuming a 5% significance level, it would be fair to conclude that null hypothesis would be rejected as the respective p value is lower than the assumed significance level. Hence, the alternative hypothesis would be accepted which implies that the weekly rent of apartments located in New Town is higher than $ 450. Hypothesis Testing Comparison of Rents The objective is to determine on the basis of the collected sample as to whether the average rent in suburb 1 (New Town) is greater than the average rent in suburb 2(Hurstville). Since inference about the population has to be drawn using sample, hence inferential statistics would be deployed. The relevant hypotheses for the given test are indicated below. Null Hypothesis (H0): New Town Hurstville Alternative Hypothesis (H1): New Town Hurstville The appropriate test to be deployed t test for 2 independent samples as the underlying standard deviation for the respective population is not known. The respective output obtained from Excel is indicated below. The relevant p value would be one tail which is 0.0499. Assuming a 5% significance level, it would be fair to conclude that null hypothesis management would be rejected as the respective p value is lower than the assumed significance level. Hence, the alternative hypothesis would be accepted which implies that the weekly rent of apartments located in New Town is higher than the weekly rent of apartments located in Hurstville. Conclusion Based on the collected sample weekly rents for apartment for the two suburbs, it would be fair to conclude that the weekly rent for apartments located in New Town (Suburb 1) would be greater than $ 450. Also, it may be concluded with 95% probability that weekly rents for apartments in New Town are comparatively higher than the corresponding values in Hurstville.