Question

Consider the following hypothesis test.

H₀: μ ≥ 50

H_a: 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.)

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

B.

x = 48 and s = 4.6

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.)

C.

x = 51 and s = 6.0

Find the value of the test statistic.

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

Answer 1

Solution :

Given that

= 50

A ) =49

S =5.2

n = 36

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :     50

Ha : < 50

Test statistic = t

= ( - ) / S / n

= (49 -50) / 5.2 / 36

= -1.154

Test statistic = t = -1.154

P-value =0.1282

= 0.01

P-value >

0.1282 > 0.01

DO NOT Reject the null hypothesis .

There is INsufficient evidence to suggest that   

B ) =48

S =4.6

n = 36

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :     50

Ha : < 50

Test statistic = t

= ( - ) / S / n

= (48 -50) / 4.6 / 36

= -2.609

Test statistic = t = -2.609

P-value =0.0066

= 0.01

P-value <

0.0066 <0.01

Reject the null hypothesis .

There is sufficient evidence to suggest that   

C ) = 51

S = 6.0

n = 36

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :     50

Ha : < 50

Test statistic = t

= ( - ) / S / n

= (51 -50) / 6.0 / 36

= 1.0

Test statistic = t = 1.0

P-value =0.8379

= 0.01

P-value >

0.8379 > 0.01

Do not reject the null hypothesis .

There is insufficient evidence to suggest that