Mat 216 GHA 2: Covers Material From OCR Chapters 10 And A

Mat 216 Gha 2this Gha Covers Material From Ocr Chapters 10 And 12

Mat 216 Gha 2this Gha Covers Material From OCR Chapters 10 and 12.

Chapter 10 introduced three hypothesis tests: the Pooled t-test, the Non-pooled t-test, and the Paired t-test. Chapter 12 introduced two hypothesis tests: the Chi-Square Goodness-of-Fit test and the Chi Square Test for Independence. For each of the three problems below, perform the appropriate test by hand and support your answer with Excel. Scan and submit work.

Be neat! Each question is worth 33 points. Good luck.

1. Researchers conducted a survey of parents of 66 kindergarten children. The parents were asked whether they played games with their children. The parents were divided into two groups: working class and middle class. The researchers wanted to know if there was an association between the frequency with which parents played games with their children and their social class. The following data were obtained: Frequency of Games Never Sometimes Often Total Middle Class Working Class Total

a) Perform a hypothesis test using the six-step critical value approach. Show all work. Be sure to include your interpretation of results in the final step. Test using α = .05.

b) Attach an Excel printout that supports your hypothesis conclusion.

2. A market research firm wants to determine whether major sports events or first-run movies attract more viewers in the prime-time hours. It selects 28 prime-time evenings; of these, 13 have sports events and the remaining 15 have first-run movies. The number of viewers for each program is recorded. If μ₁ is the mean number of sports viewers per evening of sports programming and μ₂ is the mean number of movie viewers per evening of movie programming, determine if a difference between these population means exists. Assume the population variances are equal. Test using α = .05.

Note: 1 = 6.8 million viewers; s₁ = 1.8 million viewers; 2= 5.3 million viewers; s₂= 1.6 million viewers.

a) Perform a hypothesis test using the six-step method. Show all work. Be sure to include your interpretation of results in the final step.

b) Attach an Excel printout that supports your hypothesis conclusion.

3. A new method of teaching reading to elementary students is being compared to the current standard method. Eight pairs of students with similar reading IQs are found, and one member of each pair is randomly assigned to the new method while the other is assigned to the standard method. The data in the table below support the hypothesis that the population mean test score for students taught by the new method (μ₁) is greater than the mean reading test score for those taught by the standard method (μ₂).

Perform a hypothesis test using the six-step method. Show all work. Be sure to include your interpretation of results in the final step.

Attach an Excel printout that supports your hypothesis conclusion.

Paper For Above instruction

Hypothesis Testing and Chi-Square Analyses in Social and Market Research

Understanding and applying various hypothesis tests are fundamental skills in research methodology, enabling researchers to draw valid conclusions from data. The problems outlined involve chi-square tests for independence, for goodness-of-fit, and t-tests—both independent and paired. These tests serve distinct purposes and require careful selection based on the research question and data structure.

Problem 1: Association Between Social Class and Gaming Frequency

The first problem explores whether social class influences how often parents engage in playing games with their children. A sample of 66 parents divided into middle and working-class groups provides categorical data on game frequency: Never, Sometimes, and Often. The research question seeks to determine whether there is an association between social class and gaming frequency, which is ideal for applying a Chi-Square Test for Independence.

The null hypothesis (H₀) posits no association between social class and gaming frequency; the alternative hypothesis (H₁) suggests an association exists. Using the six-step critical value approach, one must first calculate expected frequencies assuming independence, then the Chi-Square statistic by summing squared differences between observed and expected frequencies divided by expected frequencies.

If the Chi-Square statistic exceeds the critical value for the appropriate degrees of freedom at α = 0.05, we reject H₀, indicating a significant association. Conversely, failing to reject H₀ suggests independence.

Excel aids this analysis by providing functions such as CHISQ.TEST, but manual calculations reinforce understanding. The interpretation focuses on whether social class influences parental engagement in children's games, impacting parental involvement policies.

Problem 2: Comparing Viewership of Sports Events and Movies

The second problem involves comparing the mean number of viewers for sports events and movies during prime time—an independent samples problem with known variances. The data involve 13 evenings with sports and 15 with movies, with provided sample means and standard deviations.

The null hypothesis (H₀) states that there is no difference between population means (μ₁ = μ₂), while the alternative hypothesis (H₁) posits μ₁ ≠ μ₂. Assuming equal variances, the pooled t-test is appropriate. Calculating the test statistic involves the difference in sample means, pooled variance, and standard error of the difference.

If the computed t exceeds the critical t-value at α = 0.05, the null hypothesis is rejected, indicating a significant difference in average viewership. The interpretation considers the impact on broadcast strategies and advertising revenue.

Excel supports this analysis via T.TEST function, and manual calculations ensure accurate understanding. The conclusion informs broadcasters whether one type of program consistently attracts more viewers in prime time.

Problem 3: Evaluating a New Teaching Method

The third problem assesses whether a new reading method results in higher test scores compared to the standard method, using paired samples because the same nature of students and their pairing controls for confounding variables. The small sample size (n=8) calls for the paired t-test.

The hypotheses are: H₀: μ_d = 0 (no difference), H₁: μ_d > 0 (new method yields higher scores). The differences between paired scores are computed, and the mean and standard deviation of these differences are used to calculate the t-statistic.

Rejecting H₀ if the t-statistic exceeds the critical value at α = 0.05 supports the hypothesis that the new method improves reading scores. Practical significance and effect size should also be considered when interpreting results.

Excel functions like T.TEST support this analysis. This evidence informs educational practices and resource allocation for reading interventions.

Conclusion

These analysis examples highlight crucial statistical testing techniques vital for research in social sciences, marketing, and education. Carefully selecting the appropriate test based on data classification ensures valid inferences, aiding policymakers and practitioners in making informed decisions.

References

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• Hinkle, D. E., Wiersma, W., & Jurs, S. G. (2003). Applied Statistics for the Behavioral Sciences. Houghton Mifflin.
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• McClave, J. T., & Sincich, T. (2017). A First Course in Statistics. Pearson.
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