ST2120 Data were collected from a random sample of mobile phone bill pay customers in order to explore whether there is any difference in the average: Data science for business analytics II Assignment, UOG, Ireland

Question 4

Complete part (a).

(a). Data were collected from a random sample of mobile phone bill pay customers in order to explore whether there is any difference in the average length of the contract (in years) between the mainstream carriers (e.g. Eir, Vodafone, Three) and virtual operators (e.g. Tesco Mobile, GoMo, Virgin Mobile). A summary of the sample statistics and the output obtained is provided below.

(i) It is suggested to you that it is appropriate to assume the population variances are equal,
σ21 = σ2
2 Do you agree with this decision? Use the above boxplot and the following output to
support your answer, using a significance level of α = 0.05.

Levene test(Years ~ Provider, data = contracts, center = mean)

Levene’s Test for Homogeneity of Variance (center = mean)
Df F value Pr(>F)
group 1 3.1005 0.09156.
23
—
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ‘ 1

(ii) In order to carry out inference on the difference in two population means, μ1 − μ2, you will need the standard error of the difference in the means. Calculate the standard error of the difference when you assume the population variances are equal.

(iii) Using the sample statistics and the standard error from part (ii), calculate a 95% confi- dance interval for the difference in the average contract length between the mainstream and virtual mobile providers. Give an interpretation of this interval. Does the confidence interval indicate that there is a significant difference? Give a reason for your answer.

(iv) The output below gives the results for testing the hypotheses H0: μ1 − μ2 = 0 verses
Ha: μ1 − μ2 6 = 0, based on different assumptions for the population variances.
t.test(Years ~ Provider, var.equal = TRUE, data = contracts)

Two Sample t-test
data: Years by Provider
t = 2.4796, df = 23, p-value = 0.02091
alternative hypothesis: true difference in means between two groups is not equal to 0 95 percent confidence interval:
?? ??
sample estimates:
mean in group Mainstream mean in group Virtual
3.3 1.8
t.test(Years ~ Provider, var.equal = FALSE, data = contracts)

Welch Two Sample t-test

data: Years by Provider
t = 2.2504, df = 13.443, p-value = 0.04175

alternative hypothesis: The true difference in means between the two groups is not equal to 0
95 percent confidence interval:
?? ??
sample estimates:
mean in group Mainstream mean in group Virtual
3.3 1.8
Choose the appropriate set of results based on the conclusion you drew from Levene’s test in part (i). What is your conclusion from the test, at the significance level α = 0.05? Refer to the values in the appropriate output to support your
answer.
(v) Were any assumptions required in order for the analysis carried out above to be valid? If so, comment on the validity of these assumptions.