Question

Please ANSWER IN R CODE.

Problem:

Vital capacity is a measure of the amount of air that someone can exhale after taking a deep breath, Data was collected on brass players and a control group.

Brass Player	Control Group
4.7	4.2
4.6	4.7
4.3	5.1
4.5	4.7
5.5	5.0
4.9
5.3

1. Put the data into a "long format" data frame. That is one column for vital measure and second character or factor column with the label of "Brass" or "Control".
2. Conduct a test using "t.test" to determine whether the population mean for brass is larger than that for control.
3. Provide the equivalent 95% confidence interval for the difference of two population means means.
4. A researcher claims that in theory the "spread/variance" in the two populations is the same. Repeat step 2 utilizing this assumption with the argument "var.equal"

Please provide all relevant work. That is your commands, the output and any interpretations/conclusions that are necessary.

Answer 1

The R output is:

The R code is:

Brass <- c(4.7,4.6,4.3,4.5,5.5,4.9,5.3)
Control <- c(4.2,4.7,5.1,4.7,5)
t.test(Brass, Control, alternative= "greater", conf.level = 0.95)
t.test(Brass, Control, alternative= "greater", conf.level = 0.95, var.equal = TRUE)

The hypothesis being tested is:

H0: µ1 = µ2

H1: µ1 > µ2

The p-value is 0.3525.

Since the p-value (0.3525) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that the population mean for brass is larger than that for control.

The 95% confidence interval for the difference of two population means is between -0.3241937 and 0.

The hypothesis being tested is:

H0: µ1 = µ2

H1: µ1 > µ2

The p-value is 0.3577.

Since the p-value (0.3577) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that the population mean for brass is larger than that for control.

The 95% confidence interval for the difference of two population means is between -0.3394088 and 0.

Please give me a thumbs-up if this helps you out. Thank you!