Question

The average time length for students to register for summer classes at a certain college has been 50 minutes ith a standard deviation of 10 minutes. A new registration procedure using modern computing machines is being tested. If a random sample of 12 students had an average registration time of 42 minutes with a standard deviation of 11.9 minutes under the new system. Test the hypothesis that the population mean is now less than 50, using 0.05 level of significance. Assume the population of times to be normal.

Answer 1

$\mu=50 \\ \sigma= 10 \\ \bar{x}=42 \\ n= 12 \\ s=11.9 \\ H_0: \mu = 50 \\ H_1: \mu < 50$

Test-statistic:

$t = \frac{\bar{x}-\mu}{s/ \sqrt{n}} = -2.33 \\ α=0.05 \\ df=12-1=11$

One-tail test

$t_{α, df} = -1.796$

Since the value of the test statistic t=-2.33 is less than the critical value -1.796, we reject the null hypothesis and conclude that at 95% confidence level there is sufficient evidence to conclude that the population mean is now less than 50.