# Estimation and Analysis Variance

The following problems need to be worked and show work. If you report the output please, if not, just give solution to problems. OTA106049

4. A researcher has constructed an 80% confidence interval of ...

a. What would happen to the width of the interval if the researcher had used a larger sample size? (Assume other factors are held constant.)

b. What would happen to the width of the interval if the researcher had used 90% confidence instead of 80%?

c. What would happen to the width of the interval if the sample variance increased? (Assume other factors are held constant.)

(12). A developmental psychologist would like to determine how much fine motor skill improves for children from age 3 to age 4. A random sample of n=15 3 year old children and a second sample of n= 15 4 year old are obtained. Each child is give a manual dexterity test that measures fine motor skills. The average score for the older children was M= 40.6 with SS=430 and the average for the younger children was M=35.4 with SS=410. Using these data.

N1=15 N2=15

M1=40.6 M2=35.4

SS1=430 SS2=410

(a). Make a point estimate of the population mean difference in fine motor skills.

(b). Make an interval estimate so you are 95% confident that the real mean difference is in your interval.

(c). Make an interval estimate so you are 99% confident that the real mean difference is in your interval.

(d). Based on your answers from b and c, do these data indicate a significant change using a two-ailed test with a=.05? Os the difference significant with a=.01?

Chapter 13

(4). Explain why you should use ANOVA instead of several t tests to evaluate mean differences when an experiment consists of three or more treatment conditions.

(10). The following data are from an experiment comparing three treatment conditions with a separate sample of n=4 in each treatment.

(a). Use am ANOVA with a=.05 to determine whether there are any significant differences among the three treatments.

(b). Compute n2 for these data...

(14)A Researcher reports an F-Ratio with df=2,24 for an independent -measured research study.

(a). How many treatment conditions were compared in the study

(b). How many subjects participated in the entire study?

(20). The following summary table presents the results from an ANOVA comparing three treatment conditions with n=12 participants in each condition. Complete all missing values... (Hint: Start with the df Colmn).

(26). One possible explanation for why some birds migrate and others maintain year round residency in a single location is intelligence. Specifically, birds with small brains, relatively to their body size, are simply not smart enough to find food during the winter and must migrate to warmer climates where food is easily available (Sol, Lefebvre, & Rodriguex-Teijeriro, 2005). Birds with bigger brains, on the other hand, are more creative and can find food even when the weather turns harsh. Following are hypothetical data similar to relative brain size for the individual birds in each sample...

(a). Use an ANOVA with a=.05 to determine whether there are any significant mean differences among the three groups of birds.

(b). Compute n2 , the percentage of variance explained by the group differences, for these data.

(c) Use the Tukey HSD posttest to determine which groups are significantly different.

https://brainmass.com/statistics/analysis-of-variance/estimation-and-analysis-variance-316653

#### Solution Summary

Complete, Neat and Step-by-step Solutions are provided in the attached file.

ANOVA analysis: Treatment conditions, F-ratio, Migrating birds,

Estimation/Analysis of Variance

1. The following data are from an experiment comparing three treatment conditions with a separate sample of n = 4 in each treatment.

a. Use an ANOVA with a = .05 to determine whether there are any significant differences among the three treatments.

b. Compute eta2 for these data

Treatment

I II III

2 3 7 N = 12

6 7 5 G = 60

2 6 4 X2 = 344

6 4 8

M = 4 M = 5 M = 6

T = 16 T = 20 T = 24

SS = 16 SS = 10 SS = 10

2. A researcher reports an F-ratio with df - 2,24 for an independent-measures research study:

a. How many treatment conditions were compared in the study?

b. How many subjects participated in the entire study?

3. The following summary table presents the results from an ANOVA comparing three treatment conditions with n = 12 participants in each condition. Complete all missing values.

Source SS Df MS

Between Treatments ? ? 9 F = ?

Within Treatments ? ? ?

Total 117 ?

4. One possible explanation for why some birds migrate and others maintain year round residency in a single location is intelligence. Specially, birds with small brains, relative to their body size, are simply not smart enough to find food during the winter and must migrate to warmer climates where food is easily available (Sol, Lefebvre, & Rodriguez-Teijeiro, 2005). Birds with bigger brains, on the other hand, are more creative and can find food even when the weather turns harsh. Following are hypothetical data similar to the actual research results. The numbers represent relative brain size for the individual birds in each sample.

Treatment

Non-Migrating Short-Distance Migrants Long-Distance Migrants

18 6 4 N = 18

13 11 9 G = 180

19 7 5 X2 = 2150

12 9 6

16 8 5

12 13 7

M = 15 M = 9 M = 6

T = 90 T = 54 T = 36

SS = 48 SS = 34 SS = 16

a. Use an ANOVA with a = .05 to determine whether there are any significant mean differences among the three groups of birds.

b. Compute eta2, the percentage of variance explained by the group differences, for these data.

c. Use the Tukey HSD posttest to determine which groups are significantly different.