Question

7. Test H₀: π = 0.25 versus H_A: π ¹0.25 with p = 0.33 and n = 100 at alpha = 0.05 and 0.10.

8. Test at α = 0.01 the hypothesis that a majority (more than 50%) of students favor the plus/minus grading system at a university if in a random sample of 500 students, 285 favor the system?

9. Test whether the sample evidence indicates that the average time an employee stays with a company in their current positions is less than 3 years when a random sample of 64 employees yielded a mean of 2.76 years and s = 0.8. Use a= 0.01. Assume normal distribution.

Answer 1

7)
send the correct hypothesis sign will help you

8)

Hypothesis:
H0 : p = 0.50
Ha: p > 0.50

test statistics:

phat = 285/500 = 0.5700

n = 500

z = ( phat - p)/sqrt(p*(1-p)/n)
= (0.5700 - 0.50)/sqrt(0.50 *(1-0.50)/500)
= 3.1305

p value = 0.0009

P(z> 3.1305) = 1- P(z< 3.1305)
= 1- 0.9991
= 0.0009

Reject H0 as p value < 0.01

9)

Hypothesis:
H0 : mu = 3
Ha: mu < 3

tets statistics:

n = 64 , xbar = 2.76, sigma = 0.8

z = ( xbar - mu)/.(sigma/sqrt(n))
= ( 2.76 - 3)/sqrt(0.8/sqrt(64))
= -0.7589

p value = 0.2239

Do not reject H0 as pvalue > 0.01