Question

32. Ten years ago the mean number of days of skill training per year provided to employees by American businesses was 13.2. A researcher believes it to be less now. Test this assertion at the 1% level of significance, using the following information: a random sample of 49 major employers produced a mean number of days of skill training per year of 11.9 days, with standard deviation 3.4 days. (a) State the null and alternative hypotheses for the test. (b) Find the test statistic and compute its value (c) Construct the rejection region and make a decision. (d) State a conclusion in the context of the problem. (e) Compute the p-value (the observed significance) of the test.

Answer 1

(a)
H0: Null Hypothesis: $\mu$ = 13.2

HA: Alternative Hypothesis: $\mu$ < 13.2

(b)

SE= s/$\sqrt{n}$

= 3.4/$\sqrt{49}$ = 0.4857

Test statistic is given by:

t = (11.9 - 13.2)/0.4857 = - 2.6765

(c)

$\alpha$ = 0.01

ndf = n - 1 = 49 - 1 = 48

One Tail - Left Side Test

From Table, critical value of t = - 2.4066

Rejection Region:

Reject H0 if

t < - 2.4066

(d)

Since the calculated value of t = - 2.6765 is less than critical value of t = - 2.4066, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that mean number of days of skill training per year provided to employees by American businesses is less now.

(e)

t score = - 2.6765

ndf = 48

One Tail - Left Side Test

By Technology, P - Value = 0.0051

Since P - value= 0.0051 is less than $\alpha$ = 0.01, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that mean number of days of skill training per year provided to employees by American businesses is less now.