Question

In: Statistics and Probability

A group of chemists wanted to determine whether a new catalyst 2 increased the reaction rate...

A group of chemists wanted to determine whether a new catalyst 2 increased the reaction rate of a particular chemical reaction relative to that same chemical reaction with an older catalyst 1. The duration of the reactions, in seconds, are recorded below:

Catalyst 1: 14.1,18.9,22,21.2,25.3,16.8,18.7,15.3,20.4,16.6,19.5,12.9,20.6,17.2,20.4

Catalyst 2: 18.2,16.7,16.5,17.6,15.8,15.3,17.2,16,17.4,16.9

(a) Plot the data using side-by-side box plots in R.

(b) Check the assumptions for performing a two-sample t-test.

(c) Perform the appropriate two sample t test for means at the 5% level. As part of this test, specify your hypotheses, calculate a p value and make a conclusion in the context of the question. Compute the results by hand and then again using the t.test function in R.

(d) Construct and interpret a 95% confidence interval for the true difference in means (by hand and then again in R) applying the same assumptions as in part c. Describe how this confidence interval relates to your findings in part c.

Solutions

Expert Solution

The R output is:

The R code is:

Catalyst1 <- c(14.1,18.9,22,21.2,25.3,16.8,18.7,15.3,20.4,16.6,19.5,12.9,20.6,17.2,20.4)
Catalyst2 <- c( 18.2,16.7,16.5,17.6,15.8,15.3,17.2,16,17.4,16.9)
boxplot(Catalyst1)
boxplot(Catalyst2)
shapiro.test(Catalyst1)
shapiro.test(Catalyst2)
t.test(Catalyst1,Catalyst2, alternative = "greater", var.equal = TRUE, conf.level = 0.95)

(a) The side-by-side box plots are:

(b) The assumptions for performing a two-sample t-test are met.

(c) The hypothesis being tested is:

H0: µ1 = µ2

H1: µ1 < µ2

t = 1.7958, df = 23, p-value = 0.04284

Since the p-value (0.04284) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that new catalyst 2 increased the reaction rate of a particular chemical reaction relative to that same chemical reaction with an older catalyst 1.

(d) The 95% confidence interval for the true difference in means is between 0.08667833 to infinity. Since the confidence interval does not contain 0, we can conclude that new catalyst 2 increased the reaction rate of a particular chemical reaction relative to that same chemical reaction with an older catalyst 1.

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

orchestra answered 1 year ago
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