Question

Chapter 12

A researcher tested the number of mistakes made in a simulated driving test administered 15 minutes after subjects in Group C ingested the equivalent of 1.5 ounces of alcohol within 30 minutes and Group B ingested the equivalent of 3.0 ounces of alcohol within 60 minutes. Subjects’ error scores are listed below.

               Group

Control                   3.0 ounces           1.5 ounces

     A                                   B                                 C

     3                                     9                               1

     1                                   10                              0

     5                                   15                              5

     0                                   11                              2

     2                                   12                              3

     0                                   14                              6

     1                                   15                              7

     1                             16                                    8

      2                            14                        4

1. State the statistical hypothesis for this study.
2. At p<.05, state the degrees of freedom and the critical value for this statistical test.
3. Compute the F-ratio
4. Make a decision and state your conclusion in APA format (review page 389 In The Literature).
5. Indicate whether both or only one condition differs from the control group.

Chapter 13

Researchers randomly selected 5 college students and measured average minutes spent working out 8 weeks, 6 weeks, 4 weeks, and 2 weeks before Spring Break. They found the following results:

                                             Weeks

Subjects                 8              6              4              2
    A                             40            42            46            56

    B                             34            33            41            52

    C                             39            40            49            52

   D                             38            39            44            55

    E                              44            46            50            60

1. State the statistical hypothesis for this study.
2. At p<.01, state the degrees of freedom and the critical value for this statistical test.
3. Compute the F-ratio
4. Indicate effect size for this test.
5. Make a decision and state your conclusion in APA format (review page 427 In The Literature).

Answer 1

12)

For the given data, using One-way ANOVA,

a)

The hypotheses are:

Ho: µ1 = µ2 = µ3 = µ4

H1: not all means are equal

b)

Degrees of freedom: DF1 = 2, DF2 = 24

Alpha = 0.05

F Critical value = 3.403 (Using calculator)

c) F-ratio value = 58.7655 = 58.766

d)

F- value > F- critical value, so we reject H0

Reject the null hypothesis. There is suffiecient evidence to conclude that all the means are not equal

13)

Ho: µ1=µ2=µ3=µ4
H1: not all means are equal

	8 week	6 week	4 wek	2 week
count, ni =	5	5	5	5
mean , x̅ i =	39.000	40.00	40.00	55.00
std. dev., si =	3.606	4.743	12.186	3.32
sample variances, si^2 =	13.000	22.500	148.500	11.000
total sum	195	200	200	275	870	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	43.50

square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	20.250	12.250	12.250	132.250
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	101.250	61.250	61.250	661.250	885
SS(within ) = SSW = Σ(n-1)s² =	52.000	90.000	594.000	44.000	780.0000

no. of treatment , k =   4
df between = k-1 =    3
N = Σn =   20
df within = N-k =   16
  
mean square between groups , MSB = SSB/k-1 =    295.0000
  
mean square within groups , MSW = SSW/N-k =    48.7500

anova table
	SS	df	MS	F	p-value	F-critical
Between:	885.00	3	295.00	6.05	0.0059	5.29
Within:	780.00	16	48.75
Total:	1665.00	19

       α =    0.01
conclusion :    p-value<α , reject null hypothesis        
.....

F

6.05

effect size =885.00/1665.00

=0.532

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