Question

Question 5 A researcher is undertaking an early stage investigation into the possible effect of a food additive on the weight of rats. The additive is a “designer” chemical aimed at increasing growth rate. Data from the experiment are contained in the file STA201 201960 Assignment 2 Rat Diets.xlsx. (a) Show the data in a structure that allows it to be readily analysed using R Commander. (1 mark) (b) The researcher intends to determine if there is evidence that the additive has increased the weight of rats. State the appropriate null and alternate hypotheses in this instance. (c) Show the output when R Commander is used to undertake the relevant Welsch two sample t test, using a 5% level of significance. (d) Clearly state the conclusion for the test and justify this by referencing a value or values from the R Commander output. (e) State the statistical assumptions underlying Welch’s two sample t test. (f) Say if it would have been appropriate here to use the paired t test and justify your decision.

Additive	Standard
134	70
146	118
104	101
119	85
124	107
161	132
107	94
83
113
129
97
123

Answer 1

(a)

R code:

Additive <-c(134,146,104,119,124,161,107,83,113,129,97,123)
Standard <-c(70,118,101,85,107,132,94)

(b)

The Null and Alternative Hypotheses are defined as,

Where represents the mean weight for the additive group and represents the mean weight for the standard group

(c)

R Code:

t.test(Additive, Standard, alternative = "greater", mu = 0, paired = FALSE, var.equal = FALSE,conf.level = 0.95)

R Output:

Welch Two Sample t-test

data: Additive and Standard
t = 1.9107, df = 13.082, p-value =
0.0391
alternative hypothesis: true difference in means is greater than 0
95 percent confidence interval:
1.398247 Inf
sample estimates:
mean of x mean of y
120 101

(d)

Conclusion:

Since the p-value is less than 0.05 at 5% significance level, the null hypothesis is rejected.

Hence it can be concluded that the mean weight is increased in the additive group significantly compare to the standard group.

(e)

Assumption:

i) The data values are normally distributed.

ii) The variances of the two population are not equal.

(f) Say if it would have been appropriate here to use the paired t test and justify your decision. (2 marks)