5. [12 points] Minor surgery on horses under field conditions requires a reliable short-term anesthetic producing good muscle relaxation, minimal cardiovascular and respiratory changes, and a quick, smooth recovery with minimal aftereffects so that horses can be left unattended. A research article reports that, for a sample of 73 horses to which ketamine was administered under certain conditions, the sample average lying-down time was 18.9 minutes. Does this data suggest that the true mean lying-down time is less than 20 minutes? Assume that lying-down time varies according to a normal distribution with population standard deviation 8.6 minutes. Test using the level of significance α = 0.10.

Given that for a sample of 73 horses to which ketamine was administered under certain conditions, the sample average lying-down time was 18.9 minutes.

So create hypotheses as

[tex]H_o: \bar x = 20\\H_a: \bar x <20[/tex]

(left tailed test at 5% significance level)

Since population std deviation is given and sample size >30 we can useZ test

Std error = [tex]\frac{8.6}{\sqrt{73} } \\=1.007[/tex]

Z statistic = mean diff/std error

= [tex]\frac{18.9-20}{1.007} \\=-1.09[/tex]

p value one tailed = 0.138

Since p >0.05 we accept H0

i.e. there is no evidence for the data to suggest that the true mean lying-down time is less than 20 minutes