Week 3 Age Gender For The Following Questions Use Only The A ✓ Solved

Week 3agegenderfor The Following Questions Use Only The Age Column

For the following questions, use only the "age" column: 19 M 19 M Points Age Frequency Distribution: Class Width F 24 M Class Limits Midpoint Freq. Relative Frequency Cumulative Relative Freq 19 F Low High 19 M Limits ...8214 Midpoint Freq 19 F Freq. ... F Mid. .... F RF .... M CF .... M 49. F 2 Mean 24.11 Round to two decimals 58. F 2 Median 20.0 Round to one decimal 67. F 2 Sample Standard deviation: 10.39 Round to two decimals 21 F 2 Q1 19.0 Round to one decimal 19 F 2 Q3 21.8 Round to one decimal 19 F 19 M 43 M Ogive: 5 Ogive: Polygon: 19 F Polygon F 20 F 18 F 36 F Total: F 20 M 62 M 20 F Ogive 26.8 35..8 53.8 62.8 0..... Upper Limits Cummulative Relative Frequency Frequency Polygon Freq 0 22.4 31...3 58.3 67. Age Frequency Week 5 Age Gender Points 95% Confidence Interval for Average Age of Online College Students: 19 M 19 M Sample Mean: 24. F Sample St. Dev: 10. Normal Distribution 24 M 1 Sample Size: 28 T-Distribution 19 F 19 M 2 Distribution: T-Distribution 19 F 44 F 2 Critical Value: 2.05 2 decimals 19 F 20 M 2 Margin of Error: 4.03 2 decimals Calculation: 4. M 1 Lower Bound: 20.08 2 decimals Calculation: 20. F 1 Upper Bound: 28.14 2 decimals Calculation: 28. F 21 F Interpret We are 95% Confident that true mean age of all online college students lies between (20.08 yrs, 28.14 yrs) 21 F F 19 F 95% Confidence Interval for Proportion of Male Online College Students: 19 M 43 M 1 Sample Size: F 1 Number of Males: F 2 Male Proportion: 0.3571 Female Proportion 0.6429 4 decimals 20 F 18 F 2 Distribution: Normal Distribution 36 F 20 F 2 Critical Value: 1.96 2 decimals 20 M 62 M 2 Margin of Error: 0.1775 4 decimals Calculation: 0. F 1 Lower Bound: 0.1797 4 decimals Calculation: 0. Upper Bound: 0.5346 4 decimals Calculation: 0.5346 Interpret We are 95% Confident that Proportion of males in the population of all online college students lies between (0.1797, 0. Total Points Week 6 For the following two hypothesis tests, use the alpha = .05 level of confidence Points Claim: The average age of online students is 32 years old. 1 Ho: Normal Distribution 2 Ha: T-Distribution Sample mean: 24. Sample St. Dev: 10. Distribution: T-Distribution 2 Test Statistic: -2.40 2 decimals Calculation: -2. p-value: 0.0235 4 decimals 3 Interpretation: Since P value is less than 0.05 and thus reject the Null Hypothesis at % level. We conclude that there is sufficient evidence that average age of online students is different from 32 yrs old. Claim: The proportion of males in online classes is 35% 1 Ho: p = 0. Ha: p ≠0.35 Sample Proportion Males 0. Sample Proportion Females 0. Distribution: Normal Distribution 3 Test Statistic: 0.08 2 decimals Calculation: 0. p-value: 0.9368 4 decimals 3 Interpretation: Since P value is greater than 0.05 and thus we failed to reject the Null Hypothesis at 5% level. We conclude that there is insufficient evidence that proportion of males in online classes is differ from 35% 25 Total Points

Sample Paper For Above instruction

The analysis of age demographics among online college students provides valuable insights into the population’s characteristics and supports the development of targeted educational strategies. Utilizing the "age" column data, including frequency distributions, measures of central tendency, and hypothesis testing, allows for a comprehensive understanding of the age profile of these students.

The data indicates that the ages of online college students mostly cluster around the early twenties, with a mean age of approximately 24.11 years. The median age, which divides the distribution into two equal halves, is 20.0 years, suggesting a slight skew towards younger students. The standard deviation of 10.39 years reflects a wide age range, implying diversity within the population, from late teens to older adults. Such variability is essential for educators and policymakers to consider when designing courses and support services tailored to different age groups.

Frequency distributions reveal that the most common ages are around 19 and 20 years, with the age distribution displaying a right-skewed shape, as evidenced by the ogive and polygon graphs. These graphical representations articulate the cumulative age frequencies, illustrating gradual increases in the number of students as age progresses. In particular, the ogive indicates that approximately 53.8% of students are aged 20 years or younger, emphasizing a predominantly young student body.

In terms of statistical inference, constructing a 95% confidence interval for the average age of online students yielded a range between 20.08 and 28.14 years. This interval provides a high degree of certainty that the true mean age of the entire population falls within this span, with the midpoint around 24 years. The calculation involved the sample mean, standard deviation, and t-distribution critical value, acknowledging the sample size and distribution properties.

Similarly, estimating the proportion of male online college students involved calculating the sample proportion, which was approximately 35.7%. The statistical analysis employed a confidence interval for proportions, resulting in an estimated confidence interval from roughly 17.97% to 53.46%. This range encompasses the hypothesized 35%, indicating that there is not enough evidence to assert a significant difference from this proportion at the 5% significance level.

Hypothesis testing further illuminated these demographic attributes. Testing whether the average age differs from 32 years involved a t-test, producing a test statistic of -2.40 and a p-value of 0.0235. Since this p-value is less than the typical threshold of 0.05, we reject the null hypothesis, concluding that the average age of online students indeed differs significantly from 32 years. Conversely, testing the proportion of males against the hypothesized 35% yielded a non-significant result with a p-value of approximately 0.9368. This indicates insufficient evidence to conclude that the true proportion of males deviates from 35%, supporting the null hypothesis.

Overall, these statistical analyses underscore the younger age demographic prevalent in online education environments and suggest relatively balanced gender representation within the population. Such insights are crucial for tailoring online learning experiences, ensuring inclusivity, and addressing the diverse needs of students across different ages and backgrounds. Future research could expand on these findings by exploring additional demographic variables and longitudinal trends to better understand shifting patterns in online education.

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