Please show step by step on EXCEL
(a) Here as it is given that margin of error = 0.02
with 95% confidence.
so here first we will find critical test statistic for 95% confidence i.e. = NORMSINV(0.5 + 0.95/2) = NORMSINV(0.975) = 1.96 (Using Excel)
so here
margin of error = critical test statistic * standard error of sample proportion
standard error of sample proportion = sqrt [p * (1-p)/n]
here given p = 0.26
standard error = sqrt [0.26 * (1-0.26)/n]
0.02 = 1.96 * sqrt [0.26 * (1 - 0.26)/n]
n = 1847.81 or 1848
(b) Here as given point estimate = p^ = x/n = 520/1848 = 0.2814
(c) Now we would require to calculate 95% confidence interval
95% confidence interval = p^ +- MOE
Margin of error = Critical Test statistic * standard error of proportion
Critical Test statistic for 95% confidence interval = NORMSINV(0.5 + 0.95/2) = NORMSINV(0.975) = 1.96
Standard error of proportion = sqrt [0.2814 * (1 - 0.2814/1848] = 0.0105
Margin of error = 1.96 * 0.0105 = 0.0205
95% confidence interval = 0.2814 +- 0.0205 = (0.2609, 0.3019)
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