Hi there,

I am new to R and I'm having an assignment that requires the application of t-test (both independent and dependent ones). I just want to ask if the codes I used are correct or not, because the results I found were both of the hypotheses were NOT supported.

Synopsis: Suppose you have a student list with the following variables: gender (male/female), study_per_week (study hours per week), love_of_stat (love of statistics, rating 1-10), heart_rate_before (heart rate before exam), and heart_rate_after (heart rate after exam).

- You want to know if male students study significantly less hours per week than female students.

I use independent t-test with the following code:

```
t.test(study_per_week ~ gender, data = filtered_exams)
```

Here is the results for your reference:

#>

#> Welch Two Sample t-test

#>

#> data: study_per_week by gender

#> t = 1.6676, df = 55, p-value = 0.1011

#> alternative hypothesis: true difference in means between group female and group male is not equal to 0

#> 95 percent confidence interval:

#> -0.1178838 1.2866183

#> sample estimates:

#> mean in group female mean in group male

#> 3.423077 2.838710

- You want to know if students in general have significantly higher heart rate after exam compared to before exam.

I use dependent t-test with the following code:

```
t.test(
x = filtered_exams$heart_rate_before,
y = filtered_exams$heart_rate_after,
pair = TRUE )
```

here is the results for your reference:

#>

#> Paired t-test

#>

#> data: filtered_exams$heart_rate_before and filtered_exams$heart_rate_after

#> t = 16.706, df = 56, p-value < 2.2e-16

#> alternative hypothesis: true difference in means is not equal to 0

#> 95 percent confidence interval:

#> 6.531164 8.310941

#> sample estimates:

#> mean of the differences

#> 7.421053

- You want to know if the mean of the students' love of statistics is significantly lower than 5.17.

I use single sample t-test with the following code:

```
t.test(filtered_exams$love_of_stats, mu = 5.17)
```

here is the results for your reference:

#>

#> One Sample t-test

#>

#> data: filtered_exams$love_of_stats

#> t = -1.3787, df = 56, p-value = 0.1735

#> alternative hypothesis: true mean is not equal to 5.17

#> 95 percent confidence interval:

#> 3.978344 5.390077

#> sample estimates:

#> mean of x

#> 4.684211

**Note: "filtered_exams" is my new data set after removing Outliners.

So, am I using the tests correctly, or am I misunderstanding any of their characteristics?

I'm sorry if my question is a bit too long, and thank you very much for your help!

Cheers,

Esther