Question

The employees of Cybertronics Inc. need to complete a certification online. A random sample of 16 employees gives an average time for completion of all the coursework and passing the tests of 20 hours. The population standard deviation is unknown but the sample standard deviation is 6 hours. You can assume that the population of employees is fairly large. Construct a 95% confidence interval for the average time required to complete the certification.

Answer 1

Answer: $(17.06\ , 22.94)$

Step-by-step explanation:

Given : Sample size : n = 16

$\overline{x}=20$

$s= 6$

Significance level : $\alpha= 0.05$

Critical t-value : $z_{\alpha/2}=z_{0.025}=1.96$

Formula to find the confidence interval for population mean :-

$\overline{x}\pm z_{ \alpha/2}\dfrac{s}{\sqrt{n}}\\\\=20\pm (1.96)\dfrac{6}{\sqrt{16}}\\\\=20\pm2.94=(20-2.94,\ 20+2.94)\\\\=(17.06\ , 22.94)$

Hence, the 95% confidence interval for the average time required to complete the certification = $(17.06\ , 22.94)$