Question

The crew of The Enterprise on the original Star Trek series was classified among its duties by the color of its uniforms. It is a well-known trope among Star Trek fans that “Red Shirts” are expendable (there’s even a book about it!) and therefore die on away missions at a higher rate than crew of other ranks.But does that hold up under scrutiny? In a random sample of Star Trek episodes, there were 24 fatalities among 239 Red Shirt crew members; in those same episodes, there were 16 fatalities among 191 Gold and Blue Shirt crew members (i.e., “Not Red Shirt” crew

5. Construct a 95% confidence interval for the difference in fatality rates for Red Shirt and Not Red Shirt crew members.
6. Interpret the interval you found in (5). Does this interval support a large effect?
7.What are the conditions for the interval in (5) to be valid? Have they been satisfied?

Answer 1

( 5 )

( 6 )

Therefore, based on the data provided, the 95% confidence interval for the difference between the population proportions p1−p2 is −0.038<p<0.071, which indicates that we are 95% confident that the true difference between population proportions is contained by the interval (−0.038,0.071)

No interval does not support a large effect

( 5 )

As with most of the parametric procedures, we to assume that normality is met. More specifically, we require that n1p^1 = 239 * 0.9 = 23.9 ≥10  

n1(1−p^1) = 239 *( 1-0.9 ) = 23.9 ≥10

n2(p^2) = 191 *( 0.084 ) = 16.04 ≥10

n2(1−p^2) = 191 * ( 1- 0.084 ) = 174.96 ≥10

yes all the assumptions met