Question

Fashion merchandising is an industry that combines an eye for style with a nose for business. As such, those who choose to obtain a degree in fashion merchandising must study business courses as well as fashion trends. As expected, there are more women than men that study fashion merchandising in college. A random sample of 120 fashion merchandising majors shows that 75% of them are female, whereas an independent random sample of 170 business majors shows that 49% are female. We would like to estimate the true difference in proportions of females between fashion majors and business majors with 90% confidence. \

2) Calculate the margin of error. (Use a table or technology. Round your answer to three decimal places.)

3) Find the 90% confidence interval. (Round your answers to three decimal places.)

Answer 1

Solution :

Given that,

n₁ = 120

₁ = x₁ / n₁ = 0.75

n₂ =170

₂ = x₂ / n₂ = 0.49

1) Point estimate of difference between two proportions

= ₁ -  ₂

= 0.75 - 0.49

= 0.26

2)

Our aim is to construct 90% confidence interval.

c = 0.90

= 1- c = 1- 0.90 = 0.10

  /2 = 0.10 2 = 0.05

= 1.645 (use z table)

Margin of error =   *

=  

=

= 0.091

3) Required interval is

Point estimate   Margin of error

0.26    0.091

(0.26 - 0.091, 0.26 + 0.091)

(0.169 , 0.351)