Question

# ou may need to use the appropriate technology to answer this question. Consider the following hypothesis...

ou may need to use the appropriate technology to answer this question.

Consider the following hypothesis test.

H0: μ ≥ 50

Ha: μ < 50

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 = 49 and s = 5.2

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

p-value =

Do not reject H0. There is sufficient evidence to conclude that μ < 50.Reject H0. There is insufficient evidence to conclude that μ < 50.    Reject H0. There is sufficient evidence to conclude that μ < 50.Do not reject H0. There is insufficient evidence to conclude that μ < 50.

(b)

x = 48 and s = 4.5

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

p-value =

Do not reject H0. There is sufficient evidence to conclude that μ < 50.Reject H0. There is insufficient evidence to conclude that μ < 50.    Reject H0. There is sufficient evidence to conclude that μ < 50.Do not reject H0. There is insufficient evidence to conclude that μ < 50.

(c)

x = 51 and s = 6.0

Find the value of the test statistic.

p-value =

Do not reject H0. There is sufficient evidence to conclude that μ < 50.Reject H0. There is insufficient evidence to conclude that μ < 50.    Reject H0. There is sufficient evidence to conclude that μ < 50.Do not reject H0. There is insufficient evidence to conclude that μ < 50.

Solution : = 50

n = 36

This is the two tailed test .

The null and alternative hypothesis is

H0 : ≥ 50

Ha : < 50

a) = 49

s = 5.2

Test statistic = t

= ( - ) / s / n

= (49 - 50) / 5.2/ 36

= -1.154

P (t < -1.154 ) = 0.1282

P-value = 0.1282 = 0.01

p=0.1282 ≥ 0.01

-Do not reject H0. There is insufficient evidence to conclude that μ < 50.

b) = 48

s = 4.7

Test statistic = t

= ( - ) / s / n

= (48 - 50) / 4.5/ 36

= -2.667

P (t < -2.667 ) = 0.00576

P-value = 0.0058 = 0.01

p=0.0058<0.01

-Reject H0. There is sufficient evidence to conclude that μ < 50.

c) = 51

s = 6

Test statistic = t

= ( - ) / s / n

= (51- 50) /6/ 36

= 1

P (t<1 ) = 0.8379

P-value = 0.8379 = 0.01

p=0.8379 ≥ 0.01

-Do not reject H0. There is insufficient evidence to conclude that μ < 50.