Question

A survey was conducted to compare the availability of early childhood education services provided in Australia. Suppose that QLD, out of 600 households survey, 200 reported having access to early childhood education services. However, suppose in VIC, out of 900 households survey, 300 reported having access to early childhood education services.

(a) What assumption is required to carry out a hypothesis test in this case? Can you conclude from the information given that this assumption is satisfied?

(b) Test whether there is a significant difference between the proportions of households with access to early childhood education services in the two states. Use a 5% level of significance.

c) Calculate a 99% confidence interval for the difference in the proportions of households with access to early childhood education services.

d) From your answer in part (c), interpret the confidence interval you calculated.

Answer 1

a) Sample proportion of QLD is p1 = 200/600 = 0.3333
Sample proportion of VIC is p2 = 300/900 = 0.3333
n1p1 = 600*0.333 = 200 > 10 and
n1q1 = 600*(1-0.333) = 400 > 10
again
n2p2 = 900*0.333 = 300 > 10 and
n2q2 = 900*(1-0.333) = 600 > 10

Therefore, the normal conditions are satiesfied

b) H0: There is no significance difference between the proportion of QLD and VIC
H1: There is significance difference between the proportion of QLD and VIC

Let the los be alpha = 5%

Z critical value +/- = 1.96

Here Z value is lies between Z critical value so we accept H0

Thus we conclude that  there is no significance difference between the proportion of QLD and VIC

c)

d) The 99% confidence chance that the difference of proportion is lies between -0.064 and 0.064