### Statistics and Research Methodology Report

Added on - 21 Apr 2020

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Running Head: STATISTICS AND RESEARCH METHODOLOGYStatistics and Research MethodologyName of the StudentName of the UniversityAuthor Note

1STATISTICS AND RESEARCH METHODOLOGYTable of ContentsAnswer 1..........................................................................................................................................2Answer 2..........................................................................................................................................3Answer 3..........................................................................................................................................5Answer 4..........................................................................................................................................5Answer 5..........................................................................................................................................6Answer 6..........................................................................................................................................8Answer 7..........................................................................................................................................8Answer 8..........................................................................................................................................9Answer 9........................................................................................................................................10Answer 10......................................................................................................................................11Answer 11......................................................................................................................................13

2STATISTICS AND RESEARCH METHODOLOGYAnswer 1To test whether the mean balance for the store’s charge account customers is $410, a onesample t-test has to be conducted. In order to conduct the test, the null hypothesis (H0) and thealternate hypothesis (HA) has been defined as follows:Ho: μ =410HA: μ ≠410The test statistic for this test can be given by the following formula:t=́X−μσ√nHere,́Xis the sample mean,μis the mean value that has been hypothesized,σis the standarddeviation of the sample and n is the sample size. In this study,Sample mean (́X) = $511.33Hypothesized mean (μ) = $410Standard deviation of the sample (σ) = $183.75Sample size (n) = 18Degrees of freedom (n-1) = 17Level of Significance (α) = 0.05Tabulated value of the t-statistic for 18 degrees of freedom (t17,0.05) = 2.110Therefore, the t statistic can be calculated as:

3STATISTICS AND RESEARCH METHODOLOGYt=511.33−410183.75√18¿101.3319.7401¿5.133Now, it can be seen that the tabulated value of t,t17,0.05is 2.110 and the observed value oft is 5.133. Thus, the observed value of t is more than the tabulated value of t. As a result, the nullhypothesis will be rejected. Thus, it can be said thatthe manager’s claim is not supported. Thus,the auditor will have to examine all the charge account balances.Answer 2From the data, it has been observed that the average use of the service by the customersfor a sample of 15 days is 109.4. More than 100 customers are using the service daily on anaverage. Thus, it can be said that the customers like this service and use this service quite oftenas the standard deviation of the visits of the number of customers is very less (9.96).To conclude whether the mean number of customers using the self-checkout system is more than100 per day, one sample t test has to be conducted. The null hypothesis (H0) and the alternatehypothesis (HA) has been defined as follows:Ho: μ ≤100HA: μ >100The test statistic for this test can be given by the following formula:t=́X−μσ√n

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