Answer:
95% confidence interval is 15.92±1.67. Since lower confidence limit 14.25% is higher than the theoretical level 13.5%, we can reject the null hypothesis that the mean ESTAR measurements equal the theoretical level, at 0.05 significance.
Step-by-step explanation:
Confidence Interval can be calculated using M±ME where
margin of error (ME) from the mean can be calculated using the formula
ME=[tex]\frac{t*s}{\sqrt{N} }[/tex] where
Mean of the sample is=[tex]\frac{19+16+15+16.5+15+14}{6} [/tex] ≈ 15.92
Standard deviation of the sample is [tex]\sqrt{\frac{(19-15.92)^2+(16-15.92)^2+(15-15.92)^2+(16.5-15.92)^2+(15-15.92)^2+(14-15.92)^2}{6} }[/tex]≈1.59
two tailed t value of 95% confidence level in 5 degrees of freedom is 2.571
Then ME=[tex]\frac{2.571*1.59}{\sqrt{6} }[/tex] ≈ 1.67
95% confidence interval is then 15.92±1.67
Lower 95% confidence limit =14.25%
Upper 95% confidence limit= 17.59%
