Question

A web-based company has a goal of processing 95 percent of its orders on the same day they are received. If 495 out of the next 514 orders are processed on the same day, would this prove that they are exceeding their goal, using α = .025?

(a)	H0: ππ ≤ .95 versus H1: ππ > .95. Choose the right option.

a.	Reject H0 if zcalc > 1.96
b.	Reject H0 if zcalc < 1.96

	a b

(b)	Calculate the test statistic. (Round your answer to 3 decimal places.)

Test statistic

(c-1)	The null hypothesis should be rejected.
	No Yes

(c-2)	The true proportion is greater than .95.
	No evidence to support Yes

(c-3)	The company is exceeding its goal.
	No evidence to support Yes

Answer 1

Solution:

One proportion z test

Hypothesis are

H₀: π ≤ .95 versus H₁: π > .95

> sign in H1 indicates that right tailed test.

n= 514

x = 495

α = .025

Let denotes the sample proportion.

     = x/n   = 495 / 514 = 0.963

a) Critical region

For right tailed test , the critical region is >

α = 0.025 and 1 - α = 0.975

= 1.96 ..use z table

Critical region is :  Reject H₀ if z_calc > 1.96

b)The test statistic z is

z_calc =    where p = π = 0.95

= (0.963 - 0.95) / (0.95*0.05 / 514)

=  1.356

c 1) z_calc = 1.356 is less than = 1.96

So , The null hypothesis should not be rejected  

Answer is NO

c2 ) The true proportion is greater than .95.

No evidence to support

c3)  The company is exceeding its goal.

No evidence to support