A researcher would like to determine whether an over-the counter cold medication

Question

A researcher would like to determine whether an over-the counter cold medication has an effect on mental alertness. A sample of n=16 participants is obtained and each person is given a standard dose of the medication one hour before being tested in a driving simulation task. For the general population, scores on the simulation task are normally distributed with mean=60 and standard deviation=8. The individuals in the sample had an average score of M=56.5

a. State the null hypothesis
b. Compure the necessary hypothesis test using a two-tailed test with alpha=0.05. Show your calculations.
c. Make a decision about your null hypothesis. (include the critical value you used to bade your decision.)
d. Write an APA format statement summarizing your findings (include a measure of effect size if necessary.)

Explanation / Answer

Set Up Hypothesis
Null, H0: U=60
Alternate, cold medication has an effect on mental alertness H1: U!=60
Test Statistic
Population Mean(U)=60
Given That X(Mean)=56.5
Standard Deviation(S.D)=8
Number (n)=16
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=56.5-60/(8/Sqrt(16)
Zo =-1.75
| Zo | =1.75
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =1.75 & | Z | =1.96
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value : Two Tailed ( double the one tail ) - Ha : ( P != -1.75 ) = 0.0801
Hence Value of P0.05 < 0.0801, Here We Do not Reject Ho

[ANSWERS]
a. H0: U=60 , H1: U!=60
b. Zo =-1.75
c. | Z | =1.96, Do not Reject Ho
d. We conclude that cold medication has "NO EFFECT" on mental alertness

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