Question

The manager of the Groove Shopping Mall in Windhoek claims that visitors to this mall spend always more than 90 minutes in the mall on any occasion. to test this claim, the chairman of the Namibian chamber of commerce and Industry (NCCI) commissioned a study which found that, from a random sample of 25 recent visitors to this mall, the average visiting time was 95.5 minutes, with a standard deviation of 15 minutes. 2.3.1 Formulate a suitable null and alternative hypothesis for this situation 2.3.2 Compute the sample statistic 2.3.3 formulate the decision rule by using = 10% 2.3.4 What conclusion can the chairman of the Namibian Chamber of Commerce and Industry (NCCI) draw from the Findings?

Answer 1

Solution:

Given:

Claim: Visitors to this mall spend always more than 90 minutes in the mall on any occasion.

Sample size = n = 25

Sample mean = minutes

Sample standard Deviation = s = 15 minutes

Part 2.3.1)  Formulate a suitable null and alternative hypothesis for this situation

Since claim is directional to right side, this is right tailed test, thus hypothesis are:

Vs  

Part 2.3.2) Compute the sample statistic

Part 2.3.3) formulate the decision rule by using

df = n - 1 = 25 - 1 = 24

Right tail area = One tail area = 0.10

t critical value = 1.318

Thus decision rule is:

Reject null hypothesis H0, if t test statistic value > t critical value = 1.318, otherwise we fail to reject H0.

Since t test statistic value = > t critical value = 1.318, we reject null hypothesis H0.

Part 2.3.4) What conclusion can the chairman of the Namibian Chamber of Commerce and Industry (NCCI) draw from the Findings?

Since we have rejected null hypothesis H0, there is sufficient evidence to support the claim that:  visitors to this mall spend always more than 90 minutes in the mall on any occasion.