The confidence interval can be calculated by using the following formula:
`hatp+- z'(sqrt((hatp(1-hatp))/n))`
where, `hatp` is proportion of sample, n is sample size and z' is a multiplier whose value is dependent on the confidence interval. For 95% confidence interval, z can be taken as 1.96.
1) 255 students out of 458 were reportedly working.
thus, n = 458
proportion of sample, `hatp` = 255/458 = 0.557
using the equation stated above, the 95% confidence...
The confidence interval can be calculated by using the following formula:
`hatp+- z'(sqrt((hatp(1-hatp))/n))`
where, `hatp` is proportion of sample, n is sample size and z' is a multiplier whose value is dependent on the confidence interval. For 95% confidence interval, z can be taken as 1.96.
1) 255 students out of 458 were reportedly working.
thus, n = 458
proportion of sample, `hatp` = 255/458 = 0.557
using the equation stated above, the 95% confidence interval is:
`0.557 +- 1.96(sqrt((0.557(1-0.557))/458)) = 0.557 +- 0.046`
The 95% confidence interval can also be stated as [0.511,0.603]. or, we can say with 95% confidence that the proportion of the students working while studying at the start of semester I of 2014 at UC was between 0.511 and 0.603.
2) Similarly, we can solve for the 95% confidence interval of students working at the start of semester II as,
n = 490, proportion of sample, `hatp` = 250/490 = 0.510
and the 95% confidence interval is:
`0.510 +- 1.96(sqrt((0.510(1-0.510))/490)) = 0.510 +- 0.044`
The 95% confidence interval can also be stated as [0.466,0.554] or we can say with 95% confidence that the proportion of students who were working while studying at the start of second semester was between 0.466 and 0.554.
3) Since the 95% confidence intervals overlap for the two cases, we cannot make the suggestion that the proportion of students who were working while studying was higher at the start of semester I as compared to semester II.
Hope this helps.
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