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Statistics Problems Assignment

Added on - 31 May 2021

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1Statistics ProblemsStudent Name:Student ID:Due Date:Unit Name:
21.(a) Total 50 observations of the two locations, Newbury and Dedham were used for thepurpose of cross evaluation with sample proportions of returned items. It was calculatedthat there were 13NERDZERK days in Dedham compared to 7 NEDZERK days inNewbury. The detailed case explanation has been provided in table 1.It was hypothesized that proportion of NERDZERK days in Dedham and Newbury wassame. It was checked against the alternate hypothesis, where proportion of NERDZERKdays was considered unequal.A chi-square test was performed to find the test the null hypothesis using two tailed test.Value of the chi-square statistic was obtained as 0.083 with p value (0.148) greater than0.05 (Table 2). So from the test results null hypothesis could not be rejected for 5% levelof significance or type-I rate. Hence there was no significant difference in proportion ofNERDZERK days in Dedham and Newbury.Table1: NERDZERK or NOT * Location Cross-TabulationCross TabulationNewburyDedhamTotalNERDZERK71320No_ NERDZERK181230Total252550
3Table2: Chi-Square Tests of proportionChi-square Test for proportion of returnsObserved Frequency (f0)NewburyDedhamTotalNERDZERK (Obs)71320No_ NERDZERK (Obs)181230Total252550Expected Frequency (fe)NewburyDedhamTotalNERDZERK (Exp)101020No_ NERDZERK (Exp)151530Total252550χ-squareNewburyDedhamTotalNERDZERK0.90.91.8No_ NERDZERK0.60.61.2Total1.51.53P value0.08326454Non Significant(b)To test the difference in variances of returns for the two locations ANOVA was usedas an appropriate test statistic. It is a known fact that sample variance follows the chi-square distribution and ratio of the sample variances follow F –statistic. ThereforeANOVA was the best choice for this case (Sarstedt & Mooi, 2014).The F-statistic value for the model was 4.845 with p value of 0.033. The p-value was lessthan the type-I probability of 0.05. Hence the result of the test was significant. It wasconcluded that variances of returns for the two locations was significantly different.
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