Question

42. + -13 points ASWSBE14 9.E.013. You may need to use the appropriate appendix table or technology to answer this question. Consider the following hypothesis test. Hoius 50 Hu > 50 A sample of 60 is used and the population standard deviation is 8. Use the critical value approach to state your conclusion for each of the following sample results. Use a = 0.05. (Round your answers to two decimal places.) (a) x = 52.3 Find the value of the test statistic. State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the unused tail.) test statistics test statistic > State your conclusion. Reject Ho. There is insufficient evidence to conclude that u > 50. Do not reject Ho. There is sufficient evidence to conclude that u > 50. Do not reject Ho. There is insufficient evidence to conclude that u > 50. Reject Ho. There is sufficient evidence to conclude that u > 50. (b) = 51 Find the value of the test statistic. State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the unused tail.) test statistics test statistic > State your conclusion. Reject Ho. There is insufficient evidence to conclude that u > 50. Do not reject Ho. There is sufficient evidence to conclude that u > 50. Do not reject Ho. There is insufficient evidence to conclude that u > 50. O Reject Ho. There is sufficient evidence to conclude that u > 50.

Answer 1

Part a)

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 52.3 - 50 ) / ( 8 / √(60) )
t = 2.23

Critical value t(α, n-1) = t(0.05 , 60-1) = 1.67 ( From t table )

Reject null hypothesis if t > t(α, n-1)
t > t(α, n-1) = 2.227 > 1.671
Result :- Reject null hypothesis

O Reject H, There is sufficient evidence to conclude that u > 50.

Part b)

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 51 - 50 ) / ( 8 / √(60) )
t = 0.97

Critical value t(α, n-1) = t(0.05 , 60-1) = 1.67

Reject null hypothesis if t > t(α, n-1)
t > t(α, n-1) = 0.9682 < 1.671
Result :- Fail to reject null hypothesis

Do not reject H. There is insufficient evidence to conclude that p> 50.

Part c)

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 51.9 - 50 ) / ( 8 / √(60) )
t = 1.84

Critical value t(α, n-1) = t(0.05 , 60-1) = 1.67 ( from t table )

Test Criteria :-
Reject null hypothesis if t > t(α, n-1)
t > t(α, n-1) = 1.8397 > 1.671
Result :- Reject null hypothesis

Reject H. There is sufficient evidence to conclude that u > 50.