Instruction

  1. Save this file as “Math_2305_data_science_assignment_your_first_name_last_name.Rmd” (e.g., assignment4_jonny_appleseed.Rmd).

  2. For each task, provide appropriate R command(s) in the code chunk, and execute the code chunk to generate an outcome.

  3. After completing all tasks, save the your Rmd file, and produce an HTML report. 3a. Make sure to delete all intermediate code chunks before creating an HTML report.

  4. Submit your Rmd file and the rendered HTML report to D2L by its due date.

1. Load the data file (5 points)

library(tidyverse)
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.1.4     ✔ readr     2.1.5
## ✔ forcats   1.0.0     ✔ stringr   1.5.1
## ✔ ggplot2   3.5.1     ✔ tibble    3.2.1
## ✔ lubridate 1.9.4     ✔ tidyr     1.3.1
## ✔ purrr     1.0.2     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
df <- read_csv("Math 2305 Data Science Assignment_data.csv")
## Rows: 77 Columns: 17
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr  (3): county, district, grspan
## dbl (14): distcod, teachers, calwpct, mealpct, computer, testscr, compstu, e...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
df

Examine the loaded data set

2. How many rows and columns does it have? (3 points)

dim(df)
## [1] 77 17

3. Examine the first several rows of the data sets (3 points)

head(df)

4. Compute mean and standard deviation of teachers, compstu, and testscr values (4 point)

df2 <- df %>%
  summarize(mean_teachers = mean(teachers),
            sd_teachers = sd(teachers),
            mean_compstu = mean(compstu),
            sd_compstu = sd(compstu),
            mean_testscr = mean(testscr), 
            sd_testscr = sd(testscr))
df2

5. Create a scatter plot of readscr vs. mathscr (5 point)

df %>%
  ggplot(aes(x = readscr, y = mathscr)) +
  geom_point() +
  geom_smooth(method = lm) +
  labs(x = "Reading Score", y = "Math Score", title = "readscr versus mathscr")
## `geom_smooth()` using formula = 'y ~ x'

6. Compute a correlation between readscr and mathscr (30 points)

My Response:

Ho: There is no linear correlation between ‘reacscr’ and ‘mathscr’.

Ha: There is a nonzero linear positive correlation between ‘readscr’ and mathscr’.

- Report the test statistics, degree of freedom and statistical significance

My Response:

The t-statistic for the observed correlation is approximately t = 21.843. In addition, the test has 75 degrees of freedom. Furthermore, regarding the statistical significance, the p - value is extremely small, approximately 2.2e-16. Given this p-value, there’s compelling evidence against the null hypothesis, which states there is no linear correlation between reading and math scores. This suggests that the observed strong positive correlation between readscr and mathscr is statistically significant and is not a result of random variations in our sample.

- Describe the meaning of p-value in words

My Response:

The p-value tells us the probability that the observed relationship between readscr and mathscr could have happened due to random occurrences in the dataset. A small p-value (like less than 0.05) suggests that the observed relationship has statistical signifigance; this means that we can reasonably generalize this relationship to the broader population, implying it’s not just a result of random occurrences in our sample.

cor.test(df$readscr, df$mathscr)
## 
##  Pearson's product-moment correlation
## 
## data:  df$readscr and df$mathscr
## t = 21.843, df = 75, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.8911715 0.9547822
## sample estimates:
##       cor 
## 0.9295991

7. Report the findings from your correlation analysis (30 points)

My Response:

From our analysis, the test statistic is t = 21.843 with a degree of freedom of 75, and a p -value of < 2.2e-16. Given we are using a 95% confidence interval, our significance level (alpha) is 0.05. Since the p-value is much smaller than alpha, we reject the null hypothesis (Ho) in favor of the alternative hypothesis (Ha). As mentioned, this suggests a statistically significant positive linear relationship between reading and math scores (r = 0.9295991 , p < 2.2e-16)

8. Create an HTML report of your correlation analysis

Note: Professor reserves the right to decide what answers, code, and step-processs is correct not the student. Once the student submits the assignment, they are not able to resubmit for a higher grade and all grades are final when the professor inserts them in D2L.

Convert to HTML for 20 points and submit both the markdown file (.rmd) and HTML to the assignment folder in D2L.

You will have a total of 100 points for this assignment.