Question

Suppose 5% of students are veterans and 133 students are involved in sports. How unusual would it be to have no more than 8 veterans involved in sports? (8 veterans is about 6.015%)

When working with samples of size 133, what is the mean of the sampling distribution for the proportion of veterans?

When working with samples of size 133, what is the standard error of the sampling distribution for the proportion of veterans?

Compute P(ˆp≤ 0.06015).

P(ˆp≤ 0.06015) =

NOTE: Give results accurate to 5 decimal places

Is this result unusual?

• Yes, there is a less than 50% chance of this happening by random variation.
• No, there is at least a 50% chance of this happening by random variation.

Answer 1

Solution :

Given that ,

p = 0.05

1 - p = 1- = 0.95

n = 133

= p = 0.05

= (p*(1-p))/n =  (0.05*0.95)/133 = 0.01890

P( 0.06050 ) = P(( - ) / (0.06050 - 0.05) / 0.01890)

= P(z 0.556)

= 0.71090

Probability = 0.71090

No, there is at least a 50% chance of this happening by random variation.