Question

1)You are asked to conduct the following hypothesis test concerning a population mean:

H₀: µ = 68.3
H_A: µ < 68.3

You know from a previous study that σ = 7.3. You draw a sample of size 44 from the population. The mean of the sample is 66.3. Calculate the p-value for this test.

2)You are asked to conduct the following hypothesis test concerning a population mean:

H₀: µ = 67.9
H_A: µ > 67.9

You know from a previous study that σ = 4.1. You draw a sample of size 42 from the population. The mean of the sample is 68.9. Calculate the p-value for this test.

3)You are asked to conduct the following hypothesis test concerning a population mean:

H₀: µ = 32.3
H_A: µ < 32.3

You draw a sample of size 40 from the population. The mean of the sample is 30.7 and the standard deviation is 6.1. Calculate the p-value for this test.

Answer 1

Solution :

a ) Given that

= 68.3

=66.3.

=7.3

n = 44

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :    = 68.3

Ha : < 68.3

Test statistic = z

= ( - ) / / n

= (66.3.-68.3) / 7.3 / 44

= -1.82

Test statistic = z = -1.82

P(z < -1.82 ) =  0.0344

P-value = 0.0344

b ) Given that

=  67.9

= 68.9

=4.1

n = 42

This is the right tailed test .

The null and alternative hypothesis is ,

H0 :    =  67.9

Ha : >  67.9

Test statistic = z

= ( - ) / / n

= ( 68.9 - 67.9) / 4.1 / 42

= 1.58

Test statistic = z = 1.58

P(z > 1.58) = 1 - P(z < 1.58 ) = 1 -0.9429

P-value =0.0571

c ) Given that

= 32.3

=30.7

= 6.1.

n = 40

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :    = 32.3

Ha : < 32.3

Test statistic = z

= ( - ) / / n

= (30.7-32.3) / 6.1/ 40

= -1.66

Test statistic = z = -1.66

P(z < -1.66 ) =  0.0485

P-value = 0.0485