Question

A simple random sample of 100 postal employees is used to test if the average time postal employees have worked for the postal service has changed from the value of 7.5 years recorded 20 years ago. The sample mean was $download?verifier=QIf83KKkrICt6hbxAvfkRy$ = 7 years with a standard deviation of s = 2 years. Assume the distribution of the time the employees have worked for the postal service is approximately Normal. The hypotheses being tested are H₀: μ = 7.5 versus H_a: μ ≠ 7.5. A one-sample t test will be used. What is a 95% confidence interval for μ, the population mean time the postal service employees have spent with the postal service?

Group of answer choices

7 ± 2

7 ± 1.984

7 ± 0.4

7 ± 0.2

Answer 1

solutions - Given that, x = s=2 n=100 df= n-1 =100-1= 99 At a5 olo confidence level the tis L=1-95 % L=1-0.95 = 0.05 20.05 0.025 tally aft0.025; 99 = 1.984 - At a 50% confidence interval L x Î tarz! dF xs for uis L 7 I 1.984 x 2 Vloo 7 + 0.4 C 6.6 , 7.4) - A q5 % confidence interval for uis 6.6 and 7.4

7 10.4 option (c) is correct Ho:4= 7.5 Ha: el # 7.5 This is two-tailed test Tast statistic, to ensure t = 7- 7.5 2/ Vioo t= -2.5 The test statistic is -2.5 ofan-l = 100-1=99 P-value - 2x(+-2.5:94) - 2X0.0070 p-value = 0.0140 0.0140 <0.05 P-value ca Reject Ho.