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 33 14 25 33 47 Control Group 39 21 7 18 21 42 1)What is the value of the sample test statistic? (Round your answer to three decimal places.) 2)Estimate the P-value. 3)Sketch the sampling distribution and show the area corresponding to the P-value. 4) Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?? At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. 5) 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 | 55 | 33 | 14 | 25 | 33 | 47 |
| Control Group | 39 | 21 | 7 | 18 | 21 | 42 |
1)What is the value of the sample test statistic? (Round your answer to three decimal places.)
2)Estimate the P-value.
3)Sketch the sampling distribution and show the area corresponding to the P-value.
4) Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??
At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.
At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.
At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
5) 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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