Answer to Question #332232 in Statistics and Probability for pengkeee

Question

The production manager of a large manufacturing company estimates that the mean age of his employees is 22.8 years. The treasurer of the firm needs a more accurate employee mean age figure in order to estimate the cost of an annuity benefit program being considered for employees. The treasurer takes a random sample of 70 workers and finds out that the mean age of the employees sampled is 26.2 years with a standard deviation of 4.6 years. At the 0.01 level of significance, what can the treasurer conclude about the accuracy of the production manager’s estimate?

Answer 1

Step 1

$H_0:\mu=22.8$

$H_1: \mu \not=22.8$

Step 2

Type of test: two-tailed or nondirectional test. Critical value: With the use of z value table, ɑ = 0.01, two-tailed test, the critical value is z = ± 2.58

Step 3

$Z_{test}=\frac{x-\mu}{\sigma/\sqrt{n}}=\frac{26.2-22.8}{4.6/\sqrt{70}}=6.18$

$Z_{test}>Z_{critical}$ We reject H₀