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 ? = 0.01. (Let d = experimental − control.) What are we testing in this problem? paired differencesingle proportion difference of meansdifference of proportionssingle mean (a) What is the level of significance? State the null and alternate hypotheses. H0: ?d = 0; H1: ?d ≠ 0H0: ?d = 0; H1: ?d < 0 H0: ?d > 0; H1: ?d = 0H0: ?d = 0; H1: ?d > 0 (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 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 < 0.025P-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 ?? 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. (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.

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 ? = 0.01. (Let d = experimental − control.) What are we testing in this problem? paired differencesingle proportion difference of meansdifference of proportionssingle mean (a) What is the level of significance? State the null and alternate hypotheses. H0: ?d = 0; H1: ?d ≠ 0H0: ?d = 0; H1: ?d < 0 H0: ?d > 0; H1: ?d = 0H0: ?d = 0; H1: ?d > 0 (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 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 < 0.025P-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 ?? 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. (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.

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

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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	12	25	33	47
Control Group	37	21	5	18	21	42

paired differencesingle proportion difference of meansdifference of proportionssingle mean

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: ?_d = 0; H₁: ?_d ≠ 0H₀: ?_d = 0; H₁: ?_d < 0 H₀: ?_d > 0; H₁: ?_d = 0H₀: ?_d = 0; H₁: ?_d > 0

(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 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 < 0.025P-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 ??

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.

(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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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