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 FExperimental group 53 36 9 25 33 47Control Group 37 23 5 18 21 42Higher 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 α = 0.01. (Let d = experimental − control.) What are we testing in this problem?single meanpaired difference single proportiondifference of meansdifference of proportions (a) What is the level of significance? State the null and alternate hypotheses.H0: μd = 0; H1: μd ≠ 0H0: μd > 0; H1: μd = 0 H0: μd = 0; H1: μd < 0H0: μd = 0; H1: μd > 0 (b) What sampling distribution will you use? What assumptions are you making?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. The standard normal. We assume that d has an approximately uniform distribution.The Student's t. 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 P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value.WebAssign Plot WebAssign PlotWebAssign Plot WebAssign Plot (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?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.
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 53 36 9 25 33 47
Control Group 37 23 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 α = 0.01. (Let d = experimental − control.)
What are we testing in this problem?
single mean
paired difference
single proportion
difference of means
difference of proportions
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: μd = 0; H1: μd ≠ 0
H0: μd > 0; H1: μd = 0
H0: μd = 0; H1: μd < 0
H0: μd = 0; H1: μd > 0
(b) What sampling distribution will you use? What assumptions are you making?
The Student's t. We assume that d has an approximately uniform distribution.
The standard normal. We assume that d has an approximately
The standard normal. We assume that d has an approximately uniform distribution.
The Student's t. 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 P-value. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to the P-value.
WebAssign Plot WebAssign Plot
WebAssign Plot WebAssign Plot
(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?
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.
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