Question

9.66 ten engineering schools in the united states were surveyed. the sample contained 250 electrical engineers, 80 being women; 175 chemical engineers, 40 being women. compute a 90% confidence interval for the difference between the proportions of women in these two fields of engineering. is there a significant difference between the two proportions?

Answer 1

To compute the 90% confidence interval for the difference between the proportions of women in electrical and chemical engineering, you can use the formula: CI = (p1 - p2) ± z * sqrt((p1(1-p1)/n1) + (p2(1-p2)/n2)). Determine if there is a significant difference by checking if the confidence interval contains zero.

Step-by-step explanation:

To compute the 90% confidence interval for the difference between the proportions of women in electrical and chemical engineering, we can use the formula:

CI = (p1 - p2) ± z * sqrt((p1(1-p1)/n1) + (p2(1-p2)/n2))

Where:

• p1 and p2 are the proportions of women in electrical and chemical engineering respectively
• n1 and n2 are the sample sizes of electrical and chemical engineers respectively
• z is the critical value, which corresponds to a 90% confidence level

Substituting the given values, we can calculate the confidence interval:

CI = (80/250 - 40/175) ± 1.645 * sqrt((80/250(1-80/250)/250) + (40/175(1-40/175)/175))

Simplifying the equation, we can find the confidence interval.

To test if there is a significant difference between the two proportions, we can check if the confidence interval contains zero. If the confidence interval contains zero, it suggests that there is no significant difference between the proportions.