Dr. Sedaris believes that smoking cigarettes decreases a person’s sense of smell

Question

Dr. Sedaris believes that smoking cigarettes decreases a person’s sense of smell. On a standardized medical test of olfactory sensitivity, the mean sense of smell for the population is =18.4. Dr. Sedaris brings a sample of N=12 people who smoke a pack a day into his lab and measures their olfactory sensitivity. He collects the data below. Based on this information, can Dr. Sedaris conclude that smoking decreases a person's sense of smell? Use a one-tailed test with = .05. X1 = 16, X2 = 14, X3 = 19, X4 = 17, X5 = 16, X6 = 18, X7 = 17, X8 = 15, X9 = 18, X10 = 19, X11 = 12, X12 = 14

a. What are the appropriate null and alternative hypotheses?

b. What score(s) identify the appropriate critical regions?

c. What is the obtained score?

d. What is the appropriate interpretation of your results?

e. Assume we knew that the population standard deviation was = 2.05. Given this new information, again conduct the appropriate hypothesis test at =.05. Be sure to show all 4 steps for full credit.

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   18.4  
Ha:    u   <   18.4   [ANSWER]

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b)
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    11          

tcrit =    -   1.795884819      

Hence, the critical region is when t < -1.796. [ANSWER]

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c)
              
Getting the test statistic, as              
              
X = sample mean =    16.25          
uo = hypothesized mean =    18.4          
n = sample size =    12          
s = standard deviation =    2.179449472          
              
Thus, t = (X - uo) * sqrt(n) / s =    -3.417293481 [ANSWER]

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d)          
              
As t < -1.796, there is significant evidence that smoking decreases a person's sense of smell. [CONCLUSION]

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