Question

Question 4 [101 It has been established that 35% of the Small Medium Enterprises (SMES) in a certain country do comply with the International Financial Reporting Standards (IFRS). Suppose a sample of 150 SMES in the same country is collected to determine whether efforts from the National Accounting Association to create awareness improved the SMES compliance with IFRS. Required: a) Formulate the hypotheses that must be tested to determine whether the population proportion (2) of the SMES that comply with the IFRS has increased b) Suppose the sample results indicate that 60 of the SMES comply with the IFRS. Show that (4) the p-value for the hypothesis is equal to 0.1004 (2) 0.05, should the null hypothesis be rejected or not? Motivate c) At a d) Based on the hypothesis tested, what conclusion can be made about the SMES compliance (2) with the IFRS?

Answer 1

a)

Ho: p = 0.35

Ha: p > 0.35

b)

p^ = X/n = 60/150 = 0.4

TS = (p^ - p)/sqrt(pq/n) = (0.4 - 0.35)/sqrt(.35* 0.65/150) = 1.28388

p-value = P(Z > TS) = P(Z > 1.28388 ) = 0.1004

c)

since p-value > 0.05

we fail to reject the null hypothesis

d)

there is sufficient evidence that proportion has increased