Question 3: Week 8 Question 3, According to the Annual survey of drugs expenditure in country X, the annual expenditure for prescription drugs is $838 per person in the Northeast region of the country. A sample of 60 individuals in the Midwest shows a per person expenditure for prescription drugs of $745. Further, it is given that the population standard deviation of $300. V. . Based on the p value in part (II), at 99% confidence level, decide the decision criteria. v. Make the final conclusion based on the analysis.
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The provided information are:
Population mean(μ)=838Sample mean (x⎯⎯)=745Sample size(n)=60Population standard deviation(σ)=300Population meanμ=838Sample mean x¯=745Sample size(n)=60Population standard deviationσ=300
(i)
Using the provided information, the null and alternative hypotheses are:
H0:μ=838Ha:μ<838H0:μ=838Ha:μ<838
The alternative hypothesis suggests that the test is one (left) tailed.
(ii)
Here, z-test is to be used because the sample size is large and the population standard deviation is known.
(iii)
The test statistic could be calculated as:'
z===x⎯⎯−μσn√745−83830060√−2.401z=x¯-μσn=745-83830060=-2.401
Thus, the test statistic is -2.401.
Now, the p-value for left tailed test could be calculated as:
p−value ===P(Z>z)P(Z>−2.401)0.008p-value =P(Z>z)=P(Z>-2.401)=0.008
Thus, the p-value is 0.008.
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