Question

QUESTION 4 [20 MARKS]
a. Thirty women out of 100 interviewed preferred a certain lotion being manufactured at a
factory in Gaborone. A sample of 15 women was chosen. At 90% level of significance,
determine the confidence interval.             
b. The manager of a cosmetic shop believes that the average age of women who frequent the shop in 25 years. You however disagree. A sample of 51 women was taken and the average age was found to be 26.7 years with a standard deviation of 5.8 years.
i. State the Null hypothesis.           
ii. State the alternative hypothesis.           
iii. At 5% level of significance, do you reject or fail to reject the manager’s belief. (Show all workings clearly).             

Answer 1

(a)

n = 15

= 30/100 = 0.30

=0.10

From Table, critical values of Z = 1.645

Confidence Interval:

So,

Answer is:

(0.1054, 0.4946)

(b)

(i)

H0: Null Hypothesis: = 25 ( the average age of women who frequent the shop is 25 years) (Claim)

(ii)

HA: Alternative Hypothesis: 25 ( the average age of women who frequent the shop is not 25 years)

(iii)

n = 51

= 26.7

s = 5.8

=0.05

df = 51 - 1 = 50

From Table, critical values of t = 2.009

Test Statistic is given by:

Since calculated value of t is greater than critical value of t, the difference is significant. Reject null hypothesis.

Conclusion:

The data do not support the claim that the average age of women who frequent the shop is 25 years

We reject the manager's belief that the average age of women who frequent the shop is 25 years.