Consider the following hypothesis test H0 p 075 Ha p 075 A

Consider the following hypothesis test:

H0: p 0.75
Ha: p < 0.75

A sample of 300 items was selected. Compute the p-value and state your conclusion for each of the following sample results. Use = .05.

Round your answers to four decimal places.

a. p = 0.64

p-value ____

Conclusion:
p-value (greater than or equal to 0.05, rejectgreater than 0.05, do not rejectless than or equal to 0.05, rejectless than 0.05, rejectequal to 0.05, do not rejectnot equal to 0.05, do not rejectItem ) H0

b. p = 0.72

p-value_____

Conclusion:
p-value (greater than or equal to 0.05, rejectgreater than 0.05, do not rejectless than or equal to 0.05, rejectless than 0.05, rejectequal to 0.05, do not rejectnot equal to 0.05, do not rejectItem )H0

c. p = 0.7

p-value_____

Conclusion:
p-value (greater than or equal to 0.05, rejectgreater than 0.05, do not rejectless than or equal to 0.05, rejectless than 0.05, rejectequal to 0.05, do not rejectnot equal to 0.05, do not rejectItem )H0

d. p = 0.76

p-value ______

Conclusion:
p-value (greater than or equal to 0.05, rejectgreater than 0.05, do not rejectless than or equal to 0.05, rejectless than 0.05, rejectequal to 0.05, do not rejectnot equal to 0.05, do not rejectItem)H0

Solution

Consider the following hypothesis test:

H0: p 0.75
Ha: p < 0.75

A sample of 300 items was selected. Compute the p-value and state your conclusion for each of the following sample results. Use = .05.

Round your answers to four decimal places.

a. p = 0.64

p-value 0.0000

Conclusion:
p-value (less than 0.05, reject H0

Hypothesis test for proportion vs hypothesized value

Observed

Hypothesized

0.64

0.75

p (as decimal)

192/300

225/300

p (as fraction)

192.

225.

X

300

300

n

0.025

std. error

-4.40

z

5.41E-06

p-value (one-tailed, lower)

b. p = 0.72

p-value 0.1151

Conclusion:
p-value (greater than 0.05, do not reject H0

Hypothesis test for proportion vs hypothesized value

Observed

Hypothesized

0.72

0.75

p (as decimal)

216/300

225/300

p (as fraction)

216.

225.

X

300

300

n

0.025

std. error

-1.20

z

.1151

p-value (one-tailed, lower)

c. p = 0.7

p-value 0.0228

Conclusion:
p-value less than 0.05, reject H0

Hypothesis test for proportion vs hypothesized value

Observed

Hypothesized

0.7

0.75

p (as decimal)

210/300

225/300

p (as fraction)

210.

225.

X

300

300

n

0.025

std. error

-2.00

z

.0228

p-value (one-tailed, lower)

d. p = 0.76

p-value 0.6554

Conclusion:
p-value (greater than 0.05, do not reject H0

  

Hypothesis test for proportion vs hypothesized value

Observed

Hypothesized

0.76

0.75

p (as decimal)

228/300

225/300

p (as fraction)

228.

225.

X

300

300

n

0.025

std. error

0.40

z

.6554

p-value (one-tailed, lower)

Hypothesis test for proportion vs hypothesized value
	Observed	Hypothesized
	0.64	0.75	p (as decimal)
	192/300	225/300	p (as fraction)
	192.	225.	X
	300	300	n
		0.025	std. error
		-4.40	z
		5.41E-06	p-value (one-tailed, lower)