In the past, there are many studies provided strong evidence that playing chess can raise intelligence quotient (IQ) scores, strengthen problem-solving skills, enhance reading, memory, language, and foster critical, creative, and original thinking. Last year, a chess club manager, Thomas, wanted to promote his after school chess club to all parents with children attending elementary school. He wanted to show that children attending a comprehensive chess program that he created can enhance reading skills, so he decided to conducted his own study to examine the benefits for children of studying and playing chess. Thomas asked all the new chess club elementary school players (with no prior chess playing experience) whether they wanted to participate in his study. For those 55 new chess club players, he recorded their gender and asked them to take a Degree of Reading Power Test (DRP). The subjects then participated in a comprehensive chess program, and their reading performances were measured again (with DRP) after completing the program. The following is a description of the variables in the data file: Use the data to answer the following questions: 1. First you will examine the experiment design. (a) Deseribe briefly how the 55 subjects were selected in the study. Can we treat the 55 subjects as a random sample from the population of all school students? Explain why or why not? (b) Can the study be used to make conclusions about the effect of learning chess on students' reading skills? Give an example of a possible confounding factor in this study. (c) How would you redesign the experiment so that you could better assess the effect of playing chess on reading skills? 2. Do the data indicate any difference in DRP reading scores between female and male students before attending the chess program? (a) Obtain a histogram of the pre-scores for the female students and one for the male students. Use the class intervals of width 10 with bins beginning at 20 and going to 100 . The format of your histograms should include labels, title, no gaps between bars. Paste the histograms into your report. Briefly comment and compare on the shape, center and spread of the histograms. (b) Use the Descriptive Statistics feature to obtain summary statistics for the pre-scores of female students and one for the male students. Paste both summaries into your report. Do the summaries indicate any differences in DRP reading scores between the female and male students before attending the chess program? Do these summaries confirm with your finding from part (a)? (c) Use an appropriate test in Excel to see whether there was any difference in average DRP reading scores between female and male students before attending the chess program. Explain the choice of your test and discuss the assumptions necessary to apply the test. Are the assumptions satisfied in this case? You may refer to the histogram in part (a) and theory to answer the question. In particular, state the null and alternative hypotheses, report the value of the test statistic provided by the computer output, specify the distribution of the test statistic unger the null hypothesis, give the p-value of the test, and state briefly your conclusions. 3. In this part you will compare the DRP test scores with histograms. (a) Obtain histograms of the pre- and post DRP test scores for the 55 chess players used in the study. Use the class intervals of width 10 with bins beginning at 20 and going to 100 . The format of your histograms should include labels, title, no gaps between bars. Paste the two histograms into your report. (b) Comment on the shapes, centers and spreads of the histograms obtained in part (a). Do the histograms indicate that there was an overall improvement in the DRP test scores for the subjects in the study after taking the chess course? (c) Use the Descriptive Statistics feature in the Data Analysis menu to compute the summary statistics for the distributions of the pre-test and post-test scores. Paste the numerical output into your report. What do you conclude? 4. Do the data indicate an improvement in DRP reading scores for the subjects in this study after receiving the chess instruction? In order to answer the question, create a new variable of the difference between the pre-DRP test scores and the post-DRP test scores (ie. Difference = PRE-SCORE-POST-SCORE). (a) Use the Descriptive Statistics feature to obtain summary statistics for the differences. Paste the summaries into your report. Do the summaries support the claim that the subjects improved their reading scores after chess instruction? (b) Obtain a histogram of the differences. Use the class intervals of width 10 with bins beginning at - 50 and going to 20. The format of your histogram should include labels, title, no gaps between bars. Paste the histogram into your report Briefly comment on the shape of the histogram. Did all students who took the chess course improve their scores? (c) Obtain a scatterplot of the post-test scores versus the pre-test scores. Make sure that the vertical and horizontal axes have the same scales. Insert the 45-degree line in the plot; you may add the line to your plot using the drawing toolbar in Excel for this purpose. Paste the scatterplot into your report. Does the plot indicate an improvement in DRP reading scores for the students who took the chess class? Use the scatterplot to compare reading improvement of the students who did poorly on the pre-test with the improvement of the students who did very well on the pre-test. 2 5. Now you will use the inferential tools in Excel to make inferences about the data. (a) Use an appropriate test in Excel to sce whether there was an improvement in DRP scores after chess program. In particular, state the null and alternative hypotheses, report the value of the test statistic provided by the computer output, specify the distribution of the test statistic under the null hypothesis, give the p-value of the test, and state briefly your conclusions. (b) Explain the choice of your test in part (a) and discuss the assumptions necessary to apply the test. Are the assumptions satisfied in this case? You may refer to the histogram in Question 4 and theory to answer the question. (c) Use the Descriptive Statisfics feature to obtain a 95% confidence interval for the mean difference in post-and pre-test scores. Does the interval is consistent with the outcome of the test in part (a)? 6. Do the data indicate any difference in the change in DRP reading scores between female and male students after the chess program? (a) Use the Descriptive Statistics feature to obtain summary statistics for difference in DRP reading scores of female students and one for the male students. Paste both summaries into your report. Do the summaries indicate any difference in the improvement in DRP reading scores between the female and male students after the chess program? (b) Use an appropriate test in Excel to see whether there was any mean difference in the change in DRP reading scores between female and male students. In particular, state the null and alternative hypotheses, report the value of the test statistic provided by the computer output, specify the distribution of the test statistic under the null hypothesis, give the p-value of the test, and state briefly your conclusions. In the past, there are many studies provided strong evidence that playing chess can raise intelligence quotient (IQ) scores, strengthen problem-solving skills, enhance reading, memory, language, and foster critical, creative, and original thinking. Last year, a chess club manager, Thomas, wanted to promote his after school chess club to all parents with children attending elementary school. He wanted to show that children attending a comprehensive chess program that he created can enhance reading skills, so he decided to conducted his own study to examine the benefits for children of studying and playing chess. Thomas asked all the new chess club elementary school players (with no prior chess playing experience) whether they wanted to participate in his study. For those 55 new chess club players, he recorded their gender and asked them to take a Degree of Reading Power Test (DRP). The subjects then participated in a comprehensive chess program, and their reading performances were measured again (with DRP) after completing the program. The following is a description of the variables in the data file: Use the data to answer the following questions: 1. First you will examine the experiment design. (a) Deseribe briefly how the 55 subjects were selected in the study. Can we treat the 55 subjects as a random sample from the population of all school students? Explain why or why not? (b) Can the study be used to make conclusions about the effect of learning chess on students' reading skills? Give an example of a possible confounding factor in this study. (c) How would you redesign the experiment so that you could better assess the effect of playing chess on reading skills? 2. Do the data indicate any difference in DRP reading scores between female and male students before attending the chess program? (a) Obtain a histogram of the pre-scores for the female students and one for the male students. Use the class intervals of width 10 with bins beginning at 20 and going to 100 . The format of your histograms should include labels, title, no gaps between bars. Paste the histograms into your report. Briefly comment and compare on the shape, center and spread of the histograms. (b) Use the Descriptive Statistics feature to obtain summary statistics for the pre-scores of female students and one for the male students. Paste both summaries into your report. Do the summaries indicate any differences in DRP reading scores between the female and male students before attending the chess program? Do these summaries confirm with your finding from part (a)? (c) Use an appropriate test in Excel to see whether there was any difference in average DRP reading scores between female and male students before attending the chess program. Explain the choice of your test and discuss the assumptions necessary to apply the test. Are the assumptions satisfied in this case? You may refer to the histogram in part (a) and theory to answer the question. In particular, state the null and alternative hypotheses, report the value of the test statistic provided by the computer output, specify the distribution of the test statistic unger the null hypothesis, give the p-value of the test, and state briefly your conclusions. 3. In this part you will compare the DRP test scores with histograms. (a) Obtain histograms of the pre- and post DRP test scores for the 55 chess players used in the study. Use the class intervals of width 10 with bins beginning at 20 and going to 100 . The format of your histograms should include labels, title, no gaps between bars. Paste the two histograms into your report. (b) Comment on the shapes, centers and spreads of the histograms obtained in part (a). Do the histograms indicate that there was an overall improvement in the DRP test scores for the subjects in the study after taking the chess course? (c) Use the Descriptive Statistics feature in the Data Analysis menu to compute the summary statistics for the distributions of the pre-test and post-test scores. Paste the numerical output into your report. What do you conclude? 4. Do the data indicate an improvement in DRP reading scores for the subjects in this study after receiving the chess instruction? In order to answer the question, create a new variable of the difference between the pre-DRP test scores and the post-DRP test scores (ie. Difference = PRE-SCORE-POST-SCORE). (a) Use the Descriptive Statistics feature to obtain summary statistics for the differences. Paste the summaries into your report. Do the summaries support the claim that the subjects improved their reading scores after chess instruction? (b) Obtain a histogram of the differences. Use the class intervals of width 10 with bins beginning at - 50 and going to 20. The format of your histogram should include labels, title, no gaps between bars. Paste the histogram into your report Briefly comment on the shape of the histogram. Did all students who took the chess course improve their scores? (c) Obtain a scatterplot of the post-test scores versus the pre-test scores. Make sure that the vertical and horizontal axes have the same scales. Insert the 45-degree line in the plot; you may add the line to your plot using the drawing toolbar in Excel for this purpose. Paste the scatterplot into your report. Does the plot indicate an improvement in DRP reading scores for the students who took the chess class? Use the scatterplot to compare reading improvement of the students who did poorly on the pre-test with the improvement of the students who did very well on the pre-test. 2 5. Now you will use the inferential tools in Excel to make inferences about the data. (a) Use an appropriate test in Excel to sce whether there was an improvement in DRP scores after chess program. In particular, state the null and alternative hypotheses, report the value of the test statistic provided by the computer output, specify the distribution of the test statistic under the null hypothesis, give the p-value of the test, and state briefly your conclusions. (b) Explain the choice of your test in part (a) and discuss the assumptions necessary to apply the test. Are the assumptions satisfied in this case? You may refer to the histogram in Question 4 and theory to answer the question. (c) Use the Descriptive Statisfics feature to obtain a 95% confidence interval for the mean difference in post-and pre-test scores. Does the interval is consistent with the outcome of the test in part (a)? 6. Do the data indicate any difference in the change in DRP reading scores between female and male students after the chess program? (a) Use the Descriptive Statistics feature to obtain summary statistics for difference in DRP reading scores of female students and one for the male students. Paste both summaries into your report. Do the summaries indicate any difference in the improvement in DRP reading scores between the female and male students after the chess program? (b) Use an appropriate test in Excel to see whether there was any mean difference in the change in DRP reading scores between female and male students. In particular, state the null and alternative hypotheses, report the value of the test statistic provided by the computer output, specify the distribution of the test statistic under the null hypothesis, give the p-value of the test, and state briefly your conclusions