Question

7.2.13-T before the best

Answer 1

After treatment :

Sample size = n = 23

$Mean=\overline{x}=100.4min$

Standard deviation = s = 20.1 min

Confidence level = 90%

From standard normal table, the z-critical value at 90% confidence level is 1.645

Now, the 90% confidence interval estimate of mean is,

$\overline{x}\pm Z_{\alpha /2}\frac{s}{\sqrt{n}}$

$100.4\pm 1.645*\frac{20.1}{\sqrt{23}}$

$100.4\pm 6.8944$

  

( 93.5056 , 107.2944)

( 93.5 , 107.3) ( round to one decimal place)

The 90​% confidence interval estimate of the mean wake time for a population with the treatment is

93.5 min < $\mu$ < 107.3 min

The result does not suggest about the mean wake time of 105.0 minutes before the treatment because the mean wake time of 105.0 minutes is included in the 90% confidence interval which is between 93.5 min and 107.3 min. The drug does not appear effective.