Question

Consider the following hypotheses:

H₀: p ≥ 0.48

H_A: p < 0.48

Compute the p-value based on the following sample information. (You may find it useful to reference the appropriate table: z table or t table) (Round "z" value to 2 decimal places. Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

		p-value
a.	x = 50; n = 122
b.	x = 118; n = 329
c.	p⎯⎯p¯ = 0.42; n = 41
d.	p⎯⎯p¯ = 0.42; n = 413

Answer 1

Solution:

a) Here , = x/n = 50/122 = 0.41

The test statistic z is

z =   

= (0.41 - 0.48)/[0.48*(1 - 0.48)/122]

= -1.55

Here , left tailed test.

So ,

p value = P(Z < -1.55) = 0.0606

b)

Here , = 118/329 = 0.36

The test statistic z is

z =   

= (0.36 - 0.48)/[0.48*(1 - 0.48)/329]

= -4.36

Here , left tailed test.

So ,

p value = P(Z < -4.36) = 0.0000

c)

The test statistic z is

z =   

= (0.42 - 0.48)/[0.48*(1 - 0.48)/41]

= -0.77

Here , left tailed test.

So ,

p value = P(Z < -0.77) = 0.2206

d)

The test statistic z is

z =   

= (0.42 - 0.48)/[0.48*(1 - 0.48)/413]

= -2.44

Here , left tailed test.

So ,

p value = P(Z < -2.44) = 0.0073