A6 P2

A6 P2#

A generic brand of Ibuprofen is compared with the brand name Advil. 20 healthy male subjects are recruited to take the generic Ibuprofen and, once the drug has disappeared from the blood, take Advil. The blood absorption levels for each drug are recorded and summarized in the drugs.csv. We want to investigate if the blood absorption of the generic brand is, on average, is significantly different from that of Advil at a significance level of \(\alpha = 0.05\).

Summary Statistics:

Sample Size

Sample Mean

Sample Standard Deviation

20.0000

2006.1348

632.3612

20.0000

1888.6328

863.6503

Part 1#

You can read the data into R using the following code:

dat <- read.csv("drugs.csv")
x <- dat$generic
y <- dat$advil
boxplot(x,y)

Based solely on the side-by-side box plot, would you guess there will be a statistically significant result?

Answer Section#

  • No, there won’t be a statistically significant result.

  • Yes, there will be a statistically significant result.

Part 2#

What is the appropriate test of these data?

Answer Section#

  • Paired t-test

  • One Sample t-test

  • Pooled t-test

  • Welch Procedure

Part 3#

What is the null hypothesis for a two-sided hypothesis test in this context (in words)?

Answer Section#

  • The average blood absorption levels of the generic drug is the same as Advil’s.

  • The average blood absorption levels of the generic drug is greater than Advil’s.

  • The average blood absorption levels of the generic drug is less than Advil’s.

  • The average blood absorption levels of the generic drug and Advil is equal to 0.

Part 4#

What is the alternative hypothesis for a two-sided hypothesis test in this context? Let \(\mu\_{diff} = \mu_G - \mu_A\) where \(\mu_G\) is the average blood absorption of the generic brand of Ibuprofen and \(\mu_A\) is the average blood absorption of Advil.

Answer Section#

  • No, there won’t be a statistically significant result.

  • Yes, there will be a statistically significant result.

Part 5#

What is the value of pooled variance?

Answer Section#

Enter in a numeric value.

Part 6#

What is the value of the test statistic?

Answer Section#

Enter in a numeric value.

Part 7#

What is the critical value? That is, provide the (positive) value of \(t\_{crit}\) such that \(P(-t\_{crit}\) < \(T\) < \(t\_{crit}) = 1 - \alpha\) (be sure you can find this both in R and using the \(t\)-tables).

Answer Section#

Enter in a numeric value.

Part 8#

What is the appropriate test of these data?

Answer Section#

  • qt(0.025, df = 19, lower.tail = FALSE)

  • qt(0.05, df = 19)

  • qt(0.05, df = 19, lower.tail = FALSE)

  • qt(0.025, df = 39, lower.tail = FALSE)

  • pt(0.025, df = 19, lower.tail = FALSE)

Part 9#

What is the p-value?

Answer Section#

Enter in a numeric value.

Part 10#

How would this p-value be expressed based solely on the t-tables?

Answer Section#

  • p-value < 0.005

  • 0.005 < p-value < 0.01

  • 0.01 < p-value < 0.025

  • 0.025 < p-value < 0.05

  • 0.05 < p-value

Part 11#

What is the generic conclusion of the tests (select the most correct)? If we fail to reject the null hypothesis:

Answer Section#

  • We fail to reject the null at a significance level of 0.05.

  • We prove the null

  • We reject the alternative in favour of the null

  • We prove the null is true

Part 12#

What is the generic conclusion of the tests (select the most correct)? If we fail to reject the null hypothesis:

Answer Section#

  • We reject the null in favour of the alternative.

  • We reject the null

  • We reject the null in favour of the alternative at a significance level of 0.05.

  • We prove the alternative is true

Part 13#

Which of the following R code would conduct the appropriate test as found above? (All the R variables have been defined above).

Answer Section#

  • t.test(x, y)

  • t.test(x, y, var.equal = TRUE)

  • t.test(x, y, paired = TRUE)

  • t.test(mean(x), mean(y), paired = TRUE)

Part 14#

Using the output from the previous question, state the lower bound of the confidence interval for the mean difference.

Answer Section#

Enter in a numeric value.

Part 15#

State the upper bound of the confidence interval for the mean difference from the previous question.

Answer Section#

Enter in a numeric value.

Part 16#

Now suppose that the measurements in our csv file are not repeated measurements on the same individual. That is the 20 men in the generic Ibuprofen group are independent of the 20 men in the Advil group. What would be the most appropriate test in this case? Hint: your box plot will be a useful reference to help make this decision.

Answer Section#

  • t.test(x, y)

  • t.test(x, y, var.equal = TRUE)

  • t.test(x, y, paired = TRUE)

  • t.test(mean(x), mean(y), paired = TRUE)

Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.
The Creative Commons 4.0 license requiring attribution-BY, non-commercial-NC, and share-alike-SA license.