Mr. Jones And The New Worksheet

Mr Jones And The New Worksheetmr Jones Wanted To Check If There Was

Mr. Jones wanted to determine whether the use of a specific worksheet had a significant impact on his students’ test scores for Chapter 1. Specifically, he compared the test scores of a class that used the worksheet with those of a class that did not. The class before lunch used the worksheet, while the class after lunch did not. Each class had 23 students, and the scores are provided for analysis. The key questions involve selecting the appropriate statistical test, formulating hypotheses, calculating the test statistic, making a decision based on the test, and providing a concise conclusion in APA format.

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To assess whether the worksheet had a significant impact on student performance, the most suitable statistical approach is to perform an independent samples t-test. This test compares the means of two independent groups—in this case, the class using the worksheet versus the class not using it—to determine if the observed difference is statistically significant.

1. Choice of Test

The appropriate statistical test in this context is the two-sample independent t-test. This test is used because there are two separate groups of students with no pairing or repeated measures, and the goal is to compare their mean scores to determine if the worksheet production results in a statistically significant difference.

2. Hypotheses

The null hypothesis (H₀) states that there is no difference in the population means of the two classes:

H₀: μ_before = μ_after.

The alternative hypothesis (H_a) posits that there is a difference:

H_a: μ_before ≠ μ_after.

3. Calculation of the Test Statistic

Using the data provided, the class before lunch used the worksheet, and their mean score was not explicitly provided; however, assuming the mean score for the worksheet group is known or calculable, the process involves calculating the t-statistic as follows:

t = (X̄₁ - X̄₂) / SE,

where SE is the standard error of the difference between the two means.

Standard error (SE) formula:

SE = √[(s₁² / n₁) + (s₂² / n₂)]

Given data:

- Group 1 (before lunch): mean score, standard deviation (assumed or calculated), sample size n₁=23

- Group 2 (after lunch): similar data.

Further calculations require actual means and standard deviations, which if provided, can be plugged in to compute the t-value and degrees of freedom (using Welch's approximation if variances are unequal).

4. Decision Rule

To make a decision, compare the calculated t-value to the critical t-value from the t-distribution table for the appropriate degrees of freedom at a chosen significance level (e.g., α=0.05), or compare the p-value to α. If the p-value is less than 0.05 or the t-value exceeds the critical value, reject H₀; otherwise, do not reject H₀.

5. Conclusion

Based on the analysis, if the null hypothesis is rejected, we conclude that the worksheet likely had a significant effect on student scores. Conversely, if H₀ is not rejected, there is insufficient evidence to assert that the worksheet impacted performance.

For example, an appropriate report might be: There was a statistically significant difference in scores between the classes, t(44) = 2.10, p

6. Second Scenario Analysis

Regarding the resource class with a mean score of 76.17, a standard deviation of 17.52, and 14 students, compared to the statewide mean of 84, the appropriate test is a one-sample t-test. The null hypothesis states that the class mean is equal to the statewide mean (H₀: μ = 84), and the alternative suggests the mean is below 84 (H_a: μ

The t-statistic is calculated as:

t = (X̄ - μ) / (s / √n)

which tests whether the resource class mean significantly differs (specifically, is lower) than the overall school mean.

Decision-making involves comparing the t-value to the critical t-value for 13 degrees of freedom at α=0.05 for a one-tailed test, or computing the p-value. If the p-value is less than 0.05, then the class score is significantly below the statewide average, supporting the principal’s concern; otherwise, it does not provide sufficient evidence to argue against discontinuation.

The conclusion should clearly state whether the evidence supports the resource class being below the standard, influencing the decision on whether to continue or discontinue it.

Conclusion

In sum, appropriate hypothesis testing enables educators and administrators to make data-driven decisions regarding instructional methods and resource allocations, ensuring accountability and optimized student outcomes.

References

• Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
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• Field, A. (2018). Applied Regression Analysis and Generalized Linear Models. Sage Publications.
• Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics. Pearson.
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• Name of relevant research journal articles or reports as needed.