   Chapter 9.4, Problem 1LC Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

Solutions

Chapter
Section Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

A new over-the-counter cold medication includes a warning label stating that it “may cause drowsiness.” A researcher would like to evaluate this effect. It is know n that under regular circumstances the distribution of reaction times is normal with μ = 200. A sample of n = 9 participants is obtained. Each person is given the new cold medication, and. 1 hour later, reaction time is measured for each individual. The average reaction time for this sample is M = 206 with SS = 648. The researcher would like to use a hypothesis test with α = .05 to evaluate the effect of the medication.a. Use a two-tailed test with α = .05 to determine whether the medication has a significant effect on reaction time.b. Write a sentence that demonstrates how the outcome of the hypothesis test would appear in a research report.c. Use a one-tailed lest with α = .05 to determine whether the medication produces a significant increase in reaction time.d. Write a sentence that demonstrates how the outcome of the one-tailed hypothesis test would appear in a research report.

a.

To determine

To test: Whether there is any sufficient evidence to infer that the meditation has a significant effect on reaction time.

Explanation

Given info:

A two-tailed test with α=0.05 is conducted on a sample with size 9. The values of population mean, sample mean, and sum of square (SS) is given in the question as 200, 206 and 648 respectively.

Calculations:

The test hypothesis is given below:

Null Hypothesis:

H0:μ=200

Alternative Hypothesis:

H1:μ200

Degrees of freedom:

d.f=n1=91=8

Critical value:

For a one-tailed test with α=0.05 and df=8, the critical value (CV) is obtained from the t-table as CV=±2.306.

Test statistic:

The standard error s is,

s=SSn1=6488=9

Calculate the estimated standard error sm as:

sm=sn=9

b.

To determine

To find: The outcome of hypothesis test will appear in the research report.

c.

To determine
Whether the medication produces a significant increase in reaction time.

d.

To determine

To find: The outcome of hypothesis test will appear in the research report.

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