Question 1

An auditor assigned to the federal Human Resources Department is investigating applications for government assistance. The opposition in parliament claims that many applicants lack proper documentation. The auditor wants to determine the proportion of applications lacking proper documentation. Calculate the maximum number of applications that must be checked in order to determine the true proportion of applications lacking proper documentation to withing 2.35% at a 99% level of confidence. A prior estimate of the proportion is believed to have been 40%. State any assumptions you used to do this question.

Question 2

A bank manager in the town of Oistins, wished to estimate the proportion of customers who are willing to switch to online banking. Tellers are supposed to inform customers about the online banking option and get a sense of the customer's views about banking online. Although people of all ages enter the bank, it is widely believed that older individuals are less likely to accept online banking. The bank would like to reduce their hours of operation and would only open until 2:45 pm (Monday to Friday) if the proportion of older individuals who would do online banking, is more than 6% smaller than the proportion of younger individuals who would do online banking. In a survey of 200 individuals 50 years of age and older, 20 indicated they would try online banking. Seventy of 300 individuals under age 50, indicated that they would do online banking.

Use the 0.01 level of significance, to determine if the bank should only open until 2:45 PM (Monday to Friday). Use the P-Value approach.

Question 3

Nature's Fragrance makes two brands of soap: X and Y. The marketing manager wants to determine the impact of advertising on sales. In a number of stores, brand X is heavily advertised and brand Y is not advertised to the same degree. A sample of nine stores revealed the following sales figures for the two brands of soap:

X:34, 26, 36, 33, 27, 30, 22, 34, 35.

Y:29, 27, 32, 33, 23, 31, 20, 33, 31.

a) at the 0.01 level significance, is there any evidence that the average sales of brand Y are less than those of brand X? state any assumptions you used to do the question. Verify your conclusion using the p-value approach

b) what are the limitations on your conclusion in part (a)? Your answer should be specific and be in the context of this question