Question

Six sets of identical twins were randomly selected from a population of identical twins. One child was taken at random from each pair to form an experimental group. These children participated in a program designed to promote creative thinking. The other child from each pair was part of the control group that did not participate in the program to promote creative thinking. At the end of the program, a creative problem-solving test was given, with the results shown in the table below.

Twin Pair |
A |
B |
C |
D |
E |
F |

Experimental group |
55 | 35 | 14 | 25 | 33 | 47 |

Control Group |
37 | 21 | 5 | 18 | 21 | 42 |

Higher scores indicate better performance in creative problem
solving. Do the data support the claim that the program of the
experimental group did promote creative problem solving? Use
(Let

What are we testing in this problem?

single
proportionpaired
difference difference of
meanssingle
meandifference of
proportions

(a) What is the level of significance?

State the null and alternate hypotheses.
*H*_{0}:
*
μ*_{d} = 0; *H*_{1}: *
μ*_{d} < 0*H*_{0}:
*
μ*_{d} = 0; *H*_{1}: *
μ*_{d} >
0 *H*_{0}:
*
μ*_{d} > 0; *H*_{1}:
*
μ*_{d} = 0*H*_{0}:
*
μ*_{d} = 0; *H*_{1}: *
μ*_{d} ≠
0

(b) What sampling distribution will you use? What assumptions are you making?

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find (or estimate) the*P*-value.
*P*-value >
0.2500.125 < *P*-value
< 0.250 0.050 < *P*-value
< 0.1250.025 < *P*-value
< 0.0500.005 < *P*-value
< 0.025*P*-value <
0.005

Sketch the sampling distribution and show the area corresponding to the*P*-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level*
α*?

(e) Interpret your conclusion in the context of the application.

State the null and alternate hypotheses.

(b) What sampling distribution will you use? What assumptions are you making?

The
Student's *t*. We assume that *d* has an
approximately normal distribution.The standard normal. We
assume that *d* has an approximately uniform
distribution. The Student's *t*.
We assume that *d* has an approximately uniform
distribution.The standard normal. We
assume that *d* has an approximately normal
distribution.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find (or estimate) the

Sketch the sampling distribution and show the area corresponding to the

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level

At
the *
α* = 0.01 level, we reject the null hypothesis and conclude the
data are statistically significant.At the *
α* = 0.01 level, we reject the null hypothesis and conclude the
data are not statistically
significant. At the *
α* = 0.01 level, we fail to reject the null hypothesis and
conclude the data are statistically significant.At the
*
α* = 0.01 level, we fail to reject the null hypothesis and
conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient
evidence at the 0.01 to conclude that the program of the
experimental group promoted creative problem
solving.There is insufficient
evidence at the 0.01 to conclude that the program of the
experimental group promoted creative problem solving.

Answer #1

The statistical software output for this problem is:

Hence,

What are we testing? **Paired difference**

a) Level of significance = **0.01**

Hypotheses: *H*0: *μ**d* = 0; *H*1:
*μ**d* > 0

b) Sampling distribution: **Option A** is
correct.

Test statistic = **5.537**

c) P- value < 0.005

d) At the *α* = 0.01 level, we reject the null hypothesis
and conclude the data are statistically significant.

e) There is sufficient evidence at the 0.01 to conclude that the program of the experimental group promoted creative problem solving.

Six sets of identical twins were randomly selected from a
population of identical twins. One child was taken at random from
each pair to form an experimental group. These children
participated in a program designed to promote creative thinking.
The other child from each pair was part of the control group that
did not participate in the program to promote creative thinking. At
the end of the program, a creative problem-solving test was given,
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