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# Confidence Intervals of Population Mean

According to a report produced by the New South Wales Ministry of Health, 46% of hospitalisations occur in people aged sixty years and over (60+). You randomly select forty people who were hospitalized in the past year and find that fifteen of them are 60+.

a) Perform a hypothesis test at the 5% level of significance that 46% of hospitalisations occur in people aged sixty years and over. State clearly the null and alternative hypotheses, the test statistic and a conclusion in terms of the original problem, and demonstrate that any assumptions required for the test to be valid are satisfied.

b) Find a 90% confidence interval for the proportion of 60+ year old people among those hospitalized in the past year. In your answer, clearly indicate the point estimate, the estimated sampling standard deviation, the critical value from the statistical tables that was used, and the margin of error.

#### Solution Preview

(a) Ho: p is not equal to 0.46
Ha: p=0.46
This is a two tailed t test.
The degree of freedom is 39, at 0.05 significance level, the critical values are +/- 2.02.
p=15/40
the test value ...

#### Solution Summary

The confidence intervals of population mean are determined.

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