Business Analytics - Question and Answer

BUSINESS ANALYTICS
STUDENT ID:
[Pick the date]

Question 1
(a) The requisite hypotheses tested are shown below.
Null hypothesis H0 :μWellington−μChristchurch=0 i.e. there is no significant difference between sales
generated between Wellington and Christchurch
Alternative hypothesis Ha : μWellington−μChristchurch ≠0 i.e. there is significant difference between
sales generated between Wellington and Christchurch (Two Tail)
(b) The level of significance for the given test has been taken as 5%. The significance level
of 5% implies that there is a 5% chance that there is no significant difference in the sales
generated between Wellington and Christchurch when the hypothesis test indicates
otherwise. In statistical terms, it represents the probability of null hypothesis being true
when it is rejected (Flick, 2015).
(c) The independent two sample t-test output table has been obtained through the use of
Excel and is summarised below.
The t test has been used since the population standard deviation for the variables is not
known. Further, the sales generated in Wellington and Christchurch are independent of each
other. This implies that sale in one of the cities does not have any impact on the other.
Further, since the number of sample data observation for both city sales is the same and also
their variance does not differ significantly, hence equal variance test has been assumed. The
relevant p value is a two tail value which is 0.785 which is greater than the significance level
implying that null hypothesis cannot be rejected (Eriksson & Kovalainen, 2015).
(d) The critical value method is based on determining the critical value based on the level of
significance and the degree of freedom. In the given case, the degree of freedom=
(18+18) -2 = 34. The level of significance is 5%. Also, it is evident that the alternative
hypothesis is two tailed which would imply that two tailed test is to conducted. The
relevant critical values for t would be -2.032 and 2.032. Since, the computed t statistic
2