A drug company is interested in the effectiveness of a new sleeping pill. A rand

Question

A drug company is interested in the effectiveness of a new sleeping pill. A random sample of 50 people try the new sleeping pill and the number of additional hours of sleep (compared with the nights without any sleeping pill), X, are recorded. Assume that the population standard deviation of X is 3 hours. Test the hypotheses at 10% level of significance that the new drug increases the number of hours of sleep by more than 2 hours on average if the sample mean of additional hours of sleep is 2.2 hours.

Explanation / Answer

here std error of mean =std deviation/(n)1/2 =0.4243

here test stat t =(X-mean)/std errror =(2.2-2)/0.4243 =0.4714

for above for right tailed test ; and 49 degree of freedom p value =0.3197

as p vclaue is significantly higher then 0.10 level we can not reject null hypothesis.

And does not have sufficient evidence to conclude that new drug increases the number of hours of sleep by more than 2 hours on average

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