The Health Psychologist In Question Is Particularly Interest

The health psychologist in question is particularly interested in the myth of the “Freshmen 15

The health psychologist is investigating the myth that most freshmen gain weight during their first year of college, attributing this primarily to poor eating habits, lack of exercise, and insufficient sleep. To examine this, he questions whether freshmen exercise less than the general college population, which has a known mean (μ) of 100 minutes and a standard deviation (σ) of 25 minutes per week. He randomly selects a sample of 50 freshmen and records their weekly exercise minutes. The data and related questions are contained in the Excel file “Data Set 5”.

Part 1 involves constructing a 95% confidence interval for the population mean of weekly exercise minutes among freshmen. This includes inputting sample data, computing the mean, determining the alpha level, applying the CONFIDENCE function, and calculating the confidence interval limits. Additionally, five questions follow the table that need to be answered within the Excel file.

Part 2 entails hypothesis testing to assess whether freshmen exercise less than the general population. This involves formulating hypotheses, determining if the test is one-tailed or two-tailed, inputting known values (N, μ, σ), calculating the Standard Error of the Mean (σM), computing the sample mean, setting the significance level, finding the critical Z value, calculating the sample Z score, determining p-values, and answering five questions based on the statistical results.

Paper For Above instruction

The investigation into the “Freshmen 15” myth by the health psychologist provides an insightful exploration of the physical activity patterns of college freshmen compared to the general student population. By focusing on exercise as a measurable indicator, the study aims to understand whether freshmen indeed exercise less, potentially contributing to weight gain during the first year. This research employs inferential statistical methods, specifically confidence intervals and hypothesis testing, to analyze the sample data and draw meaningful conclusions about the population parameters.

Construction of a 95% confidence interval is foundational in estimating the true average of weekly exercise minutes among freshmen. The process involves first ascertaining the sample size (N = 50) and the known population standard deviation (σ = 25). Using Excel's AVERAGE function on the raw data allows for the precise calculation of the sample mean (M). The alpha level, representing the probability of a Type I error, is set at 0.05 for this confidence interval, aligning with standard research conventions.

The CONFIDENCE function in Excel calculates the margin of error for the interval, which, when added to and subtracted from the sample mean, yields the lower and upper bounds of the confidence interval. This range provides a plausible estimate of the true mean exercise time per week for all freshmen at the college. Interpreting this interval can assist in understanding whether freshmen, on average, meet or fall below normative activity levels, potentially informing interventions to promote healthier lifestyles.

Following the confidence interval analysis, hypothesis testing offers a more specific evaluation of whether freshmen exercise significantly less than the general population mean (μ = 100). The null hypothesis (H0) states that the mean exercise time for freshmen is equal to the population mean (μ = 100), while the alternative hypothesis (H1) posits that freshmen exercise less (

Determining the test's parameters involves inputting known values, with N = 50, μ = 100, and σ = 25. The Standard Error of the Mean (σM) is computed as σ divided by the square root of N, which is essential for standardization in the Z-test. Calculation of the sample mean (M) from raw data supports this process, ensuring accuracy in the subsequent statistical steps.

Using an alpha level of 0.05, the critical Z value is derived through Excel's NORMSINV function, considering the tail's direction based on the hypothesis. The Z score for the sample is then calculated by subtracting the hypothesized mean from the sample mean and dividing this difference by the Standard Error. This Z score indicates how many standard errors the sample mean is from the hypothesized mean, serving as the test statistic.

The p-value associated with the observed Z score quantifies the probability of obtaining a result as extreme or more extreme under H0. Comparing the p-value to the alpha threshold informs whether to reject H0. In this scenario, a p-value less than 0.05 provides evidence that freshmen exercise significantly less than the general population mean, supporting the hypothesis that they may be at risk for weight gain due to lower activity levels.

Overall, this statistical analysis integrates confidence interval estimation and hypothesis testing techniques to scrutinize the myth of the “Freshmen 15.” It highlights the importance of empirical data in challenging or confirming societal beliefs about college student behaviors. Such research informs campus health initiatives and can guide policies promoting physical activity among students, ultimately contributing to healthier college environments.

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