41. Use problem number 20 on page 9-21 to answer to following questions (a-h). a) What is the sample mean b) What is the sample standard deviation c) Use Z or T test? And why? d) What is your hypothesis test e) At = 0.05, what is the rejection rule when using the method you choose in (C)? f) Compute the value of the test statistic. g) What is the p-value? h) What is your conclusion? 42. Use problem number 18 on page 9-21 to answer the following questions (a-e). a) Use Z or T test? And why? c) Compute the value of the test statistic. e) What is your conclusion? b) At = 0.05, what is the rejection rule? d) What is the p-value? 43. Use problem number 2 on page 10-27 to answer the following questions (a-d). a) Write and interpret the estimated regression equation c) Compute the F statistic and test the significance of the relationship at a .05 level of significance b) What is the number of observations d) Predict monthly maintenance expense for any terminal that is used 25 hours per week a) Sample mean (x) = (108 + 118+ 120 +122 +119 + 113 + 124 + 122 + 120 + 123) / 10.= 118.9 b) Sample standard deviation = 4.93 c) here, we are using t test because sample size is less than 30 d)Null Hypothesis H0: Alternative Hypothesis Ha : e) at alpha 0.05 we reject the null hypothesis when p vlue is less than alpha. f) Test statistic= ( x - m ) / (s / sqrt(n)) = (118.9 - 120)/(4.93/ sqrt(10)) = -0.70 g) P value is calculated by using t statistic with degree of freedom (10 -1) = 9 P value = 0.5016 h) Here, p value is greater than alpha 0.05 so, we fail to reject the null hypothesis. (a) Use t test because the population standard deviation is unknown and the sample size < 30 (b) Rejection Rule: = 0.05 Degrees of freedom = 25 - 1 = 24 Critical t- score = 1.710882067 Reject Ho if t > 1.710882067 (c) Data: n = 25 = 110 s = 10 x-bar = 115 Hypotheses: Ho: 110 Ha: > 110 Test Statistic: SE = s/n = 10/25 = 2 t = (x-bar - )/SE = (115 - 110)/2 = 2.5 (d) p- value = 0.009827087 (e) Decision (in terms of the hypotheses): Since 2.5 > 1.710882067 we reject Ho and accept Ha Conclusion (in terms of the problem): There is evidence that the mean is greater than 110 43 (a) y = 6.1092+0.8951*x (b)the value of the t test statistic: t=0.8951/0.149 =6.01 the p-value = P(t with df=n-2=8 > 6.01) = 0.0002 We can conclude that monthly maintenance expense is related to usage (c)6.1092+0.8951*25 =28.4867