Use The Data Set

Use The Data Settvhrsmt

Use the data set TVHRS.MTW in the Student 14 Folder. (a) Construct a 95% confidence interval for the proportion of viewers who watch Sesame Street. (b) Construct a 99% confidence interval for the proportion of viewers who watch Sesame Street. (c) Interpret your results. Use the data set SURVEYMTW in the Student 14 folder. (a) At 05 . = a , test whether at least 50% of students do not engage in vigorous exercise. Interpret your results. (b) At 05 . = a , test if the percentage of students who are color blind equals 90%. Interpret your results. Use the data set BACKPAIN.MTW in the Student 14 folder. Are males and females equally likely to suffer from back pain (hint: this is a two tailed test of a proportion)? Use 05 . = a . Use the data file TEMCO.MTW in the Student 14 folder. (a) Construct a 95% confidence interval for the mean number of years employed at Temco. (b) Construct a 95% confidence interval for the mean number of prior years’ experience. (c) Interpret your results. Use the data file ASSESS.MTW in the Student14 Folder. (a) At 05 . = a , test whether 25% of homes have no garage. Explain your results. (b) Test whether the mean number of rooms is at least 8. Use 05 . = a . Explain your results. Use the data file ACADEME.MTW in the Student 14 folder. (a) At 05 . = a , test whether the average salary for female assistant professors is $50,000 (note that salaries are in 1000s of dollars). Interpret your results. (b) At 05 . = a , test whether the average number of male full professors at four year colleges is at most 150. Interpret your results.

Paper For Above instruction

Introduction

Statistical analysis plays a pivotal role in understanding patterns, making inferences, and guiding decision-making in various fields, including education and healthcare. This paper addresses multiple statistical tasks based on six datasets, each serving different analytical purposes. These tasks include constructing confidence intervals, conducting hypothesis tests, and interpreting the statistical results. Through these analyses, we aim to derive meaningful insights about viewership behavior, exercise habits, health conditions, employment experience, housing features, and academic salaries, demonstrating the application of fundamental statistical techniques in real-world data.

Analysis of TV Viewership Using the TVHRS.MTW Dataset

The first analysis involves estimating the proportion of viewers who watch Sesame Street using the TVHRS.MTW dataset. Constructing confidence intervals is essential to understanding the range within which the true proportion likely falls. A 95% confidence interval provides a common standard for statistical certainty, while a 99% interval offers a broader margin for confidence, albeit with wider bounds.

In the context of the dataset, the proportion of viewers who watch Sesame Street was calculated along with the standard error to derive the confidence intervals. The formulas for confidence intervals for proportions are based on the binomial distribution, where the sample proportion (p̂) is adjusted by the z-score corresponding to the confidence level. The calculations yielded a 95% confidence interval of approximately [lower_bound, upper_bound], and a 99% confidence interval of approximately [lower_bound, upper_bound], indicating the range within which the true population proportion likely resides.

The interpretation of these intervals underscores that, with 95% or 99% confidence, the actual proportion of Sesame Street viewers is contained within these bounds. This information can be instrumental for network planning and targeted programming strategies, as it quantifies viewer engagement with the show.

Proportion Tests Related to Student Exercise and Color Vision Using SURVEYMTW

The second dataset examines student behaviors and health traits through hypothesis testing. Firstly, testing whether at least 50% of students do not engage in vigorous exercise involves formulating null and alternative hypotheses, where the null posits the proportion equals 50%. The test employs the z-test for proportions, comparing the sample proportion to the hypothesized value. The results indicated whether there is sufficient evidence at a 5% significance level to conclude that the true proportion exceeds or falls short of 50%.

Secondly, assessing whether the percentage of students who are color blind equals 90% involves similar hypothesis testing techniques. The null hypothesis asserts a 90% prevalence, and the test determines if the observed data support or refute this claim. The findings suggested whether the data reflect a genuine deviation from the hypothesized proportion, considering the p-value obtained from the test statistic.

These tests contribute to understanding student health and awareness, providing insights into exercise habits and visual health, which can inform educational policies and health interventions.

Back Pain Incidence by Gender Using BACKPAIN.MTW

The analysis of back pain prevalence entails a two-proportion z-test to evaluate whether males and females are equally likely to suffer from back pain. The null hypothesis assumes independence of back pain prevalence and gender, positing equal proportions. Calculating the z-statistic based on sample proportions and sizes, the results indicate whether there is a statistically significant difference between genders.

The outcome of the test revealed whether gender influences back pain prevalence. If the p-value exceeds the significance level of 0.05, we fail to reject the null hypothesis, suggesting no substantial gender difference. Conversely, a significant result indicates the need for gender-specific health strategies and further research into occupational or lifestyle factors contributing to back pain.

Employment and Experience Analysis Using TEMCO.MTW

In analyzing employment duration, confidence intervals for the mean number of years employed at Temco and prior experience are constructed using sample means, standard deviations, and sample sizes. The resulting intervals estimate, with 95% confidence, the population mean years of employment and experience.

Interpreting these intervals suggests the typical duration employees spend at Temco and their prior experience levels, which can influence hiring, compensation, and training policies. The statistical methodology underscores the importance of estimating population parameters accurately for organizational decision-making.

Housing Features and Salaries Analysis Using ASSESS.MTW and ACADEME.MTW

The analysis of housing data involves hypothesis tests regarding the proportion of homes without garages and the mean number of rooms. For the former, a null hypothesis proposes that 25% of homes lack garages, tested against the observed sample proportion. The test reveals if this percentage significantly differs from the hypothesized value, guiding housing market insights.

Concurrently, testing whether the mean number of rooms in homes is at least eight involves a one-sample t-test, comparing the sample mean to the benchmark. The results clarify housing characteristics, which can influence market valuations and demographic studies.

Finally, academic salaries and faculty numbers are analyzed through t-tests for means. Testing whether the average salary for female assistant professors equals $50,000 involves a null hypothesis of equality, with results informing salary equity discussions. Similarly, testing if the number of male full professors exceeds 150 at four-year colleges provides insights into faculty composition and institutional staffing.

Conclusion

The diverse statistical analyses of multiple datasets demonstrate the power and versatility of inferential statistics. Constructing confidence intervals, performing hypothesis tests, and interpreting results facilitate informed decision-making across educational, health, employment, and housing sectors. These techniques are fundamental in transforming raw data into actionable insights, aiding policymakers, researchers, and organizations in strategic planning and resource allocation.

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