Reserve Bank of Australia (RBA) 22.5% of Australian families are maintaining private insurances in addition to the government Medicare health scheme. RBA has also reported that the rate of using private insurance has been increasing from the last ten years and assume a team of researchers willing to test the following hypotheses.

H_o: μ 22.5

H_a: μ < 22.5

Assume, the research group surveyed a sample of 50 families and found that 20.25% of them are using private insurances in addition to the government Medicare health scheme.

I. What is the value of the test statistic if the population standard deviation is 6.25%?

II. What is the p-value?

III. At α =.05, what is your conclusion?

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