Question

Consider the following hypothesis test.

H₀: μ ≥ 35

H_a: μ < 35

A sample of 36 is used. Identify the p-value and state your conclusion for each of the following sample results. Use

α = 0.01.

(a)

x = 34 and s = 5.2

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.) *PLEASE GO INTO DETAIL WHEN EXPLAINING THIS STEP! How do you know if it is to the left or right tail of the test statistic?*

p-value =

(b)

x = 33 and s = 4.5

Find the value of the test statistic. (Round your answer to three decimal places.)

-2.667

Find the p-value. (Round your answer to four decimal places.)

p-value =

C.)

x = 36 and s = 5.0

Find the value of the test statistic.

1.2

Find the p-value. (Round your answer to four decimal places.)

p-value =

Answer 1

Solution :

= 35

n = 36

Df = n-1 = 36 -1 = 35

This is the left tailed test .

The null and alternative hypothesis is

H₀ :    ≥ 35

H_a : < 35

a) x = 34 and s = 5.2

Test statistic = t

= ( - ) / s / n

= (34 - 35) /5.2 / 36

= -1.154

P (Z < -1.154 ) = 0.1282

P-value = 0.1282

= 0.01  

0.1282 > 0.01

Do not reject the null hypothesis .

There is insufficient evidence to suggest that

(b)

x = 33 and s = 4.5

Test statistic = t

= ( - ) / s / n

= (33 - 35) /4.5 / 36

= -2.667

P (Z < -1.154 ) = 0.0058

P-value = 0.0058

= 0.01

0.0058 < 0.01

Reject the null hypothesis .

There is sufficient evidence to suggest that

c)

x = 36 and s = 5.0

The test statistic is = 1.2

P (Z < 1.2 ) = 0.8809

P-value = 0.8809

= 0.01  

0.8809 > 0.01

Do not reject the null hypothesis .

There is insufficient evidence to suggest that