Answered: An article reported the results of a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

An article reported the results of a peer tutoring program to help children learn to read. In the experiment, the children were randomly divided into two groups: the experimental group received peer tutoring along with regular instruction, and the control group received regular instruction with no peer tutoring. There were n₁ = n₂ = 36 children in each group. The Gates-MacGintie Reading Test was given to both groups before instruction began. For the experimental group, the mean score on the vocabulary portion of the test was x₁ = 344.5, with sample standard deviation s₁ = 45.5. For the control group, the mean score on the same test was x₂ = 334.3, with sample standard deviation s₂ = 48.5. Use a 10% level of significance to test the hypothesis that there was no difference in the vocabulary scores of the two groups before the instruction began.

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: ?₁ = ?₂; H₁: ?₁ > ?₂H₀: ?₁ = ?₂; H₁: ?₁ < ?₂ H₀: ?₁ ≠ ?₂; H₁: ?₁ = ?₂H₀: ?₁ = ?₂; H₁: ?₁ ≠ ?₂

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

The standard normal. Both sample sizes are large with unknown standard deviations.The Student's t. Both sample sizes are large with unknown standard deviations. The standard normal. Both sample sizes are large with known standard deviations.The Student's t. Both sample sizes are large with known standard deviations.

What is the value of the sample test statistic? (Test the difference ?₁ − ?₂. 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.

(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 ? = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

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

Reject the null hypothesis, there is insufficient evidence that there is a difference in mean vocabulary scores between the control and experimental groups.Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean vocabulary scores between the control and experimental groups. Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean vocabulary scores between the control and experimental groups.Reject the null hypothesis, there is sufficient evidence that there is a difference in mean vocabulary scores between the control and experimental groups

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