A study was designed to measure the effect of home environment on academic achievement of 12-year-old students. Because genetic differences may also contribute to academic achievement, the researcher wanted to control for this factor. Thirty sets of identical twins were identified who had been adopted prior to their first birthday, with one twin placed in a home in which academics were emphasized (Academic) and the other twin placed in a home in which academics were not emphasized (Nonacademic). The final grades (based on 100 points) for the 60 students are given here. Set of Twins Academic Nonacademic 1 78 71 2 75 70 3 68 66 4 92 85 5 55 60 6 74 72 7 65 57 8 80 75 9 98 92 10 52 56 11 67 63 12 55 52 13 49 48 14 66 67 15 75 70 16 90 88 17 89 80 18 73 65 19 61 60 20 76 74 21 81 76 22 89 78 23 82 78 24 70 62 25 68 73 26 74 73 27 85 75 28 97 88 29 95 94 30 78 75 a. Is there a difference in the mean final grades between the students in an academi- cally oriented home environment and those in a nonacademically oriented home environment. Use a = .05. b. Estimate the size of the difference in the mean final grades of the students in academic and nonacademic home environments using a 95% confidence interval. c. Do the conditions for using the t procedures appear to be satisfied for these data? d. Does it appear that using twins in this study to control for variation in final scores was effective as compared to taking a random sample of 30 students in both types of home environments? Justify your answer.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

See similar textbooks

Related questions

Question

A study was designed to measure the effect of home environment on academic achievement of 12-year-old students. Because genetic differences may also contribute to academic achievement, the researcher wanted to control for this factor. Thirty sets of identical twins were identified who had been adopted prior to their first birthday, with one twin placed in a home in which academics were emphasized (Academic) and the other twin placed in a home in which academics were not emphasized (Nonacademic). The final grades (based on 100 points) for the 60 students are given here.

Set of Twins	Academic	Nonacademic
1	78	71
2	75	70
3	68	66
4	92	85
5	55	60
6	74	72
7	65	57
8	80	75
9	98	92
10	52	56
11	67	63
12	55	52
13	49	48
14	66	67
15	75	70
16	90	88
17	89	80
18	73	65
19	61	60
20	76	74
21	81	76
22	89	78
23	82	78
24	70	62
25	68	73
26	74	73
27	85	75
28	97	88
29	95	94
30	78	75

a. Is there a difference in the mean final grades between the students in an academi- cally oriented home environment and those in a nonacademically oriented home environment. Use a = .05.

b. Estimate the size of the difference in the mean final grades of the students in academic and nonacademic home environments using a 95% confidence interval.

c. Do the conditions for using the t procedures appear to be satisfied for these data?

d. Does it appear that using twins in this study to control for variation in final scores was effective as compared to taking a random sample of 30 students in both types of home environments? Justify your answer.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Anova and Design of Experiments$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.