To test the effect of alcohol in increasing the reaction time to respond to a gi

Question

To test the effect of alcohol in increasing the reaction time to respond to a given stimulus, the reaction times of seven people were measured. After consuming 3 ounces of 40% alcohol, the reaction time for each of the seven people was measured again. Do the following data indicate that the mean reaction time after consuming alcohol was greater than the mean reaction time before consuming alcohol? Use

= 0.05. (Use

before after = d.

Round your answers to three decimal places.)

1-2. Null and alternative hypotheses:

A) H0: d = 0 versus d 0

B) H0: d = 0 versus d < 0    

C) H0: d = 0 versus d > 0

D) H0: d < 0 versus d > 0

E) H0: d 0 versus d = 0

3. Test statistic:  t =

5. Conclusion:

A) H0 is rejected. There is insufficient evidence to indicate that the mean reaction time is greater after consuming alcohol.

B) H0 is not rejected. There is insufficient evidence to indicate that the mean reaction time is greater after consuming alcohol.    

C) H0 is rejected. There is sufficient evidence to indicate that the mean reaction time is greater after consuming alcohol.

D) H0 is not rejected. There is sufficient evidence to indicate that the mean reaction time is greater after consuming alcohol.

Person   1     2     3     4     5     6     7   Before 3 4 4 5 3 7 3 After 6 9 2 5 3 6 5

Explanation / Answer

The t-Statistics for difference of Means is given by

t = (Sample Mean of x - Sample Mean of y) - (Population Parameter of x - Population Parameter of y ) / [S1/sqrt1/n1 + S2/sqrt1/n2)]

Where S1 and S2 are the sample mean square variances.

If Population parameter of x = Population Parameter of y, then

t = (Sample mean of x - Sample Mean of y)/ [S1/sqrt1/n1 + S2/sqrt1/n2)]

Here we are assuming x = before and y = after

So, t = (1.464 -2.268)/(1.464/sqrt(7) +2.268/sqrt(7))

   = -0.709

Under the given condition Coclusion (D) is true.

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