Answer to Question #318792 in Statistics and Probability for vii

Question

One of the undersecretary of the Department of Labor and

Employment (DOLE) claims that the average salary of civil engineer

is Php18,000. A sample of 19 civil engineer’s salary has a mean of

Php17,350 and a standard deviation of Php1,230. Is there enough

evidence to reject the undersecretary’s claim at α = 0.01?

Answer 1

Hypothesized Population Mean $\mu=18000$

Sample Standard Deviation s=1230

Sample Size n=19

Sample Mean $\bar{x}=17350$

Significance Level $\alpha=0.01$

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

$H _ 0 ​ :μ=18000$

$H _ 1 ​ :μ \not= 18000$

This corresponds to two-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.

Based on the information provided, the significance level is $\alpha=0.01$

$df=n−1=18$

degrees of fredom, and the critical value for two-tailed test is

$t_c=2.87844$

The rejection region for this left-tailed test is $R=\{t:|t|>2.87844\}$

The tt - statistic is computed as follows: $t=\frac{x-\mu}{s/\sqrt{n}}=\frac{17350-18000}{1230/\sqrt{19}}=-2.30348$

Since it is observed that

$|t|=2.30348<2.87844=t_c$

it is then concluded that the null hypothesis is not rejected.

Therefore, there is not enough evidence to claim that the population mean $\mu$ is different than 18000, at the $\alpha=0.01$

significance level.

Using the P-value approach: The p-value for two-tailed, the significance level

$\alpha=0.01, df=18, t=-2.30348$

is p=0.033425 and since

$p=0.033425>0.01=\alpha$

it is concluded that the null hypothesis is not rejected.

Therefore, there is not enough evidence to claim that the population mean $\mu$ is different than 18000, at the $\alpha=0.01$

significance level.