Question

A sample of size 25 was obtained to test the given hypotheses. Calculate the p-value for each of the sample results in parts a through c Ho p 0.27 HA p0.27 - p 0.09 a. p-value (Round to three decimal places as needed.) b. p 0.3 p-value (Round to three decimal places as needed.) c. p 0.37 p-value (Round to three decimal places as needed.) d. p 0.47 p-value (Round to three decimal places as needed.)

Answer 1

Answer:

a)

Given,

n = 25

p = 0.27

q = 1 - p

= 1 - 0.27

q = 0.73

p^ = 0.09

Z = (p^ - p)/(sqrt(pq/n))

substitute the values

= (0.09 - 0.27)/sqrt(0.27*0.723/25)

= (- 0.18/0.088792)

Z = - 2.0272

Corresponding p value is 0.043 [Since from z table & rounded to three decimal places]

b)

p^ = 0.31

Z = (p^ - p)/(sqrt(pq/n))

substitute the values

Z = (0.31 - 0.27)/sqrt(0.27*0.73/25)

= 0.04/0.088792

Z = 0.4505

P value = 0.652 [Since from z table & rounded to three decimal places]

c)

p^ = 0.37

Z = (p^ - p)/(sqrt(pq/n))

substitute the values

Z = (0.37 - 0.27)/sqrt(0.27*0.73/25)

= 0.1 / 0.088792

Z = 1.1262

P value = 0.260 [Since from z table & rounded to three decimal places]

d)

p^ = 0.47

Z = (p^ - p)/(sqrt(pq/n))

substitute the values

Z = (0.47 - 0.27)/sqrt(0.27*0.73/25)

= 0.2/0.088792

Z = 2.2525

P value = 0.024  [Since from z table & rounded to three decimal places]