Consider the following hypotheses: H0: 70.1 HA: > 70.1 A sample of 31 observatio

Question

Consider the following hypotheses: H0: 70.1 HA: > 70.1 A sample of 31 observations yields a sample mean of 71.1. Assume that the sample is drawn from a normal population with a known population standard deviation of 5.7. Use Table 1. a. Calculate the p-value. (Round "z" value to 2 decimal places.) p-value b. What is the conclusion if = 0.05? Reject H0 since the p-value is greater than . Reject H0 since the p-value is smaller than . Do not reject H0 since the p-value is greater than . Do not reject H0 since the p-value is smaller than . c. Calculate the p-value if the above sample mean was based on a sample of 136 observations. (Round "z" value to 2 decimal places.) p-value d. What is the conclusion if = 0.05? Reject H0 since the p-value is smaller than . Reject H0 since the p-value is greater than . Do not reject H0 since the p-value is smaller than . Do not reject H0 since the p-value is greater than .

Explanation / Answer

(a)

Data:    

n = 31   

= 70.1   

s = 5.7   

x-bar = 71.1   

Hypotheses:    

Ho: 70.1   

Ha: > 70.1   

Decision Rule:    

= 0.05   

Critical z- score = 1.644853627   

Reject Ho if z > 1.644853627   

Test Statistic:    

SE = s/n = 5.7/31 = 1.023750222

z = (x-bar - )/SE = (71.1 - 70.1)/1.02375022155262 = 0.98

p- value = 0.164333899   

(b) Do not reject H0 since the p-value is greater than

(c)

Data:

n = 136

= 70.1

s = 5.7

x-bar = 71.1

Hypotheses:

Ho: 70.1

Ha: > 70.1

Decision Rule:

= 0.05

Critical z- score = 1.644853627

Reject Ho if z > 1.644853627

Test Statistic:

SE = s/n = 5.7/136 = 0.488770968

z = (x-bar - )/SE = (71.1 - 70.1)/0.48877096765615 = 2.05

p- value = 0.020380742

(d) Reject H0 since the p-value is smaller than .

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