Statistics Study Material

STATISTICS

Question 1:
a. Provide a 95% confidence interval for all the patients who are referred to
the health centre by the hospital.
From the provided information,
Sample size of patients (n) = 400
80 were referred by the local hospital that is x = 80
Sample proportion can be obtained as:
Confidence level = 95%
The Z value at 95% confidence level from the standard normal table is 1.96.
The required 95% confidence interval can be obtained as:
Thus, the required confidence interval is 0.161 to 0.239.

b. What sample size would be required to estimate the proportion of all
hospital referrals to the health centre with a margin of error of 0.04 or less at
95% confidence?
Given E=0.04
So, n = (Z/E)^2*p*(1-p)
Where;
E = Margin of error;
P = Probability of occurring an error
= (1.96/0.04)^2*0.2*0.8
=384.16
Take n=385
Therefore the sample size required at margin of error of 0.04 or less at 95% confidence level will
be 385.
Question 2:
Step 1. Statement of the hypothesis
Determine the statement of the hypothesis.
The statement of the hypothesis is generally indicated by the null hypothesis which is determined
below:
That is, there is no evidence that there has been a significant increase in the starting salaries of
students who graduated from colleges of Business in 2009.