Answer to Question #153799 in Statistics and Probability for marites valencia

Question

 In a time motion study, it was found that a certain manual work can be finished at an average time of 40 minutes with a standard deviation of 8 minutes. A group of 16 students is given a special training and then found the average is only 35 minutes. Can we conclude that the special training can speed up the work using 0.01 level?

a.      Formulate the null hypothesis

b.     Select an appropriate alternative hypothesis

c.      Determine the level of significance to be used

d.     Choose an appropriate test statistics and determine the critical value of the test statistics

e.     Find the value of the test statistics using the sample date

f.       Make a decision, reject H_o if the absolute computed value of the test statistics is greater than the absolute critical value, otherwise accept H_o

Answer 1

a. H₀: $\mu=40$

b. H₁: $\mu<40$

c. $\alpha=0.01$

d. We use z-statistics

For $\alpha=0.01$ and left-tailed test critical value = -2.326

e. Computing test value:

z=$\frac{\overline{X}-\mu}{\sigma/\sqrt{n}}=\frac{35-40}{8/\sqrt{16}}=-2.5$

f. Since absolute computed value of the test statistics is greater than the absolute critical value we should reject H_o.

We can conclude that the special training speed up the work using $\alpha=0.01$