Question

What proportion of college students plan to major in Business? You survey a random sample of 250 first-year college students, and you find that 57 of these students indicate they plan to pursue a major in Business. Use this information to construct a 90% confidence in order to estimate the population proportion of college students who plan to major in Business.

Answer 1

Solution :

Given that,

n = 250

x = 57

= x / n = 57 /250 = 0.228

1 - = 1 - 0.228 = 0.772

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.645 * (((0.228 * 0.772 ) / 250)

= 0.044

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.228 - 0.044 < p < 0.228 + 0.044

0.184 < p < 0.272

The 90% confidence interval for the population proportion p is : ( 0.184 , 0.272)