Question

Question 6 (11) Two headache remedies claim to give fast acting relief. An experiment was performed to compare the mean lengths of time required for bodily absorption of brand A and brand B headache remedies. Twelve people were randomly selected and given an oral dose of Brand A and another 12 were randomly selected and given an equal dose of brand B. Each group's results are shown below: Brand A Brand B Sample mean 21.8 min 18.9 min Sample standard deviation 8.7 min 7.5 min Test the claim that there is no difference in the mean time required for bodily absorption. a) What is the null hypothesis? b) Compute the test statistic c) Estimate the p-value d) Conclude and interpret the results e) If the o is known how would the estimation differ? (3) mãe

Answer 1

a) Hypothesis

Ho:$\mu$₁=$\mu$₂

H₁: $\mu$_1$\neq$$\mu$_2. Where
ul, u2
are population mean of absorb time for brand A and B respectively

b) Test statistic has t distribution with df 12-1=11.

Under Ho,Test statistic=(21.8-18.9)/

8.72/12+7.52 /12

=0.874

c) p value=2P[T>0.874]=2*0.2=0.4 where T has t distribution with df 11.

d)As p value is greater than alpha(0.05) we failed to reject Ho. That means we do not have enough evidence to conclude that two headache remedies are statistically significant in respect of mean time require for bodily absorption.

e) If sigma is known then our test statistic will have standard normal distribution.If we consider our sigma is known and they are 8.7 and 7.5, then our p value will change a bit.P value=2P(Z>0.874)=2*0.19=0.38.So our test report will be same.

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