For aspirin manufacturers, the goal is to alleviate headaches with a mean relief

Question

For aspirin manufacturers, the goal is to alleviate headaches with a mean relief times of 50 minutes. In the population, headache relief times are considered to be sufficiently Normally Distributed. In a test involving Brand Aspirin, given to 20 subjects, the mean relief times was 48 minutes with a standard deviation of 3.5 minutes. Using alpha = 0.01, can it be concluded that Brand A Aspirin relieves headaches in less than 50 minutes? Use the 10-step hypothesis testing procedure, (If an approximate p-value cannot be determined from the Z cumulative probability table, use bracketing in the t probability table to estimate the p-value range.)

Explanation / Answer

here std error =std deviation/(n)1/2 =0.7826

hence test stat t =(X-mean)/std error =(48-50)/0.7826=-2.5556

for above p value =0.0097

as p vlaue is less then 0.01 level we reject that mean is equal to 50 and conclude that sufficient evidence to accept that mean is less then 50

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