Week 3 Age Gender For The Following Questions Use Onl 985607 ✓ Solved

Week 3agegenderfor The Following Questions Use Only The Age Column

For the following questions, use only the "age" column: the dataset includes ages of online college students, with a sample mean of 24.11 years, a median of 20.0 years, and a sample standard deviation of 10.39 years. The sample size is 28 students. The ages range from 19 to 49 years, with frequency distributions, cumulative frequencies, and relative frequencies provided. Descriptive statistics and confidence intervals are calculated, including a 95% confidence interval for the average age, which is between 20.08 and 28.14 years, and a confidence interval for the proportion of male students, which ranges from approximately 17.97% to 53.46%. Hypothesis tests are conducted at the 0.05 significance level to determine if the average age differs from 32 years and if the proportion of male students is 35%. The test for mean age yields a sample mean of 24 with a standard deviation of 10, leading to a test statistic and p-value that inform whether to accept or reject the null hypothesis. Similarly, the test for the proportion of males involves comparing the sample proportion (approximately 35.71%) to the hypothesized 35%, using a z-test with calculated p-values to interpret the results.

Sample Paper For Above instruction

Introduction

Understanding the demographic characteristics of online college students is essential for educational planning, resource allocation, and policy development. Among these characteristics, age and gender distribution offer insights into student diversity and help tailor academic support services. This paper presents a comprehensive statistical analysis focusing solely on the "age" column of the dataset, utilizing descriptive statistics, confidence intervals, and hypothesis testing to explore the average age and gender proportions within the sampled population of online learners.

Descriptive Statistics and Data Overview

The dataset comprises ages of 28 online college students, with ages ranging from 19 to 49 years. The mean age is calculated at 24.11 years, indicative of a relatively young student body. The median age, at 20.0 years, suggests a concentration of students concentrated around their early twenties. The ages' distribution exhibits a standard deviation of 10.39 years, reflecting variability within the cohort. Such descriptive measures provide foundational insights into the age demographics, informing subsequent statistical analysis.

The frequency distribution reveals the distribution of ages across specific classes, with class widths and midpoints calculated for clarity. The dataset indicates a larger proportion of students clustered around the younger age brackets, with frequencies declining in higher age ranges. The cumulative frequency and relative frequency distributions further elucidate the demographic spread, which is critical for understanding the overall age profile of online students.

Confidence Interval for Mean Age

Using the sample mean and standard deviation, and assuming the distribution of ages follows a normal distribution or T-distribution due to the sample size, a 95% confidence interval for the true mean age was calculated. The critical t-value for 27 degrees of freedom at a 95% confidence level is approximately 2.05. The margin of error (ME) was computed as 4.03, leading to a confidence interval bounded between 20.08 and 28.14 years.

This interval indicates that we are 95% confident that the true average age of online college students lies within this range. The lower bound (20.08 years) suggests that the mean age is somewhat lower than the hypothesized 32 years, hinting at a predominantly younger student demographic in online courses.

Analysis of Gender Proportions

The dataset also provides information on gender distribution, with 36% of the sample identified as male, and 64% as female. Using these proportions, a confidence interval was constructed to estimate the true proportion of males in the entire online student population. With a sample proportion of approximately 0.3571, and employing a critical value of 1.96, the margin of error was calculated at 0.1775, resulting in a 95% confidence interval between roughly 17.97% and 53.46%.

This wide interval underscores uncertainty regarding the gender composition, but it suggests that the true proportion of males in the population could be as low as approximately 18% or as high as 53%. The sample proportion being close to 35% indicates that males are a minority within this online student cohort.

Hypothesis Testing: Mean Age

To assess whether the average age of online students differs from 32 years, a hypothesis test was conducted at the 0.05 significance level. The null hypothesis (H₀) states that the mean age is 32 years, while the alternative hypothesis (H₁) posits that it is not.

Using the sample mean (24), standard deviation (10), and sample size (28), the t-test statistic was calculated as approximately -4.34. The corresponding p-value, derived from the t-distribution with 27 degrees of freedom, is less than 0.001. Given the p-value is significantly below the alpha threshold, we reject H₀, concluding that the average age of online students is statistically different from 32 years, specifically younger.

Hypothesis Testing: Proportion of Males

The second hypothesis test examined whether the proportion of male students is 35%. The null hypothesis asserts that the proportion is 0.35, against the alternative that it differs. The observed sample proportion is approximately 0.3571.

Calculating the z-statistic yielded a value near 0.064, with a p-value of approximately 0.948. Since this p-value exceeds 0.05, we fail to reject the null hypothesis, implying insufficient evidence to suggest the proportion of males differs from 35%. Therefore, the data supports the assumption that about 35% of online students are male.

Conclusion

The statistical analyses collectively reveal that the average age of online college students is significantly younger than 32 years, with a 95% confidence interval suggesting an average between approximately 20 and 28 years. This indicates a predominantly younger demographic within online learning environments. Additionally, the proportion of male students aligns closely with the hypothesized 35%, and the data does not provide enough evidence to refute this assumption.

These insights are valuable for educational institutions aiming to tailor their online programs to the demographic characteristics of their student populations. Recognizing that online learners are generally younger and that gender proportions are relatively balanced supports targeted support strategies and marketing approaches aligned with student demographics.

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