# Calculation of type I and type II error

2. Two different companies have applied to provide cable television service in a certain region. Let p denote the proportion of all potential subscribers who favor the first company over the second. Consider testing H0 : p = .5 vs HA : P ≠ .5 based on a random sample of 25 individuals. Let X denote the number in the sample who favor the first company and x represent the observed value of X.

i. Which of the following rejection regions is most appropriate and why?

R1 = {x : x < 7 or x > 18}

R2 = {x : x < 8}

R3 = {x : x>17}

ii. In the context of this problem situation, describe what type I and type II errors

are.

iii. Compute the probability of a type II error for the selected region in part (a)

when p = .3, p = .4, p = .5, and p = .6.

https://brainmass.com/statistics/type-i-and-type-ii-errors/calculation-type-type-error-72111

#### Solution Preview

i)

Consider 95% confidence interval

P( |x - np / √npq | < 1.96) = .95

|x - 25*0.5 / √25*.5*.5 | < 1.96

|x - 12.5 / 2.5 | < 1.96

| x - 12.5 | < 4.9

-4.9 < x - 12.5 ...

#### Solution Summary

The solution calculates type I and type II error.