Question

Consider the following hypothesis test:

H₀ : u = 100

H_a : u not equal to 100

A sample of 80 is used. Identify the -value and state your conclusion for each of the following sample results. Use a=0.05 . Round the value of the test statistic to three decimal places. If required enter negative values as negative numbers.

a. x bar = 115 and s = 12

t-value
p-value	- Select your answer -lower than .01, between .01 and .025, between .025 and .05, between .05 and .10. between .10 and .20, greater than .20
conclusion	- Select your answer -do not reject, reject

b. x bar = 106.5 and s = 10.5

t-value
p-value	- Select your answer -lower than .01, between .01 and .025, between .025 and .05, between .05 and .10, between .10 and .20, greater than .20
conclusion	- Select your answer -do not reject, reject

c. x bar = 113 and s = 12.5

t-value
p-value	- Select your answer -lower than .01, between .01 and .025, between .025 and .05, between .05 and .10, between .10 and .20, greater than .20
conclusion	- Select your answer -do not reject, reject

Answer 1

Solution :

a) = 100

= 115

s = 12

n = 80

This is the two tailed test .

The null and alternative hypothesis is

H₀ :   = 100

H_a :    100

Test statistic = t

= ( - ) / s / n

= (115-100) / 12 / 80

= 11.18

p(Z > 11.18 ) = 1-P (Z < 11.18 ) = 0

P-value = 0.0000

= 0.05  

p=0<0.05

lower than .01,

Reject .

b)

= 106.5

s = 10.5

This is the two tailed test .

The null and alternative hypothesis is

H₀ :   = 100

H_a :    100

Test statistic = t

= ( - ) / s / n

= (106.5-100) / 10.5 / 80

= 5.537

p(Z > 5.537 ) = 1-P (Z < 5.537) = 0

P-value = 0.0000

= 0.05  

p=0<0.05

lower than .01,

Reject .

c)

= 106.5

s = 10.5

This is the two tailed test .

The null and alternative hypothesis is

H₀ :   = 100

H_a :    100

Test statistic = t

= ( - ) / s / n

= (113-100) / 12.5 / 80

=9.302

p(Z > 9.302 ) = 1-P (Z < 9.302) = 0

P-value = 0.0000

= 0.05  

p=0<0.05

lower than .01,

Reject .