Question

In the Introductory Survey we asked if you had paid employment while studying at university. We also asked this question in the equivalent survey for Semester 2 2018. A summary of the results for this question from both surveys is shown in the table below. ‘Working’ denotes students who said that they had some kind of paid employment while studying, ‘Total’ denotes the total number of students who responded to these questions in the surveys. 2019 Semester 1 Working 355 Total 627 2018 Semester 2 250 510 STAT101 includes a very wide range of students. For this question we will assume that these samples can be regarded as random samples from the total populations of first year UC students in Semester 1 2019 and Semester 2 2018, respectively. a) Use the data to construct a 90% confidence interval for the population proportion of first year UC students who were working while studying at the start of Semester 1 2019. b) Use the data to construct a 90% confidence interval for the population proportion of first year UC students who were working while studying at the start Semester 2 2018. c) Use your confidence intervals to comment on the suggestion that the proportion of first year UC students who were working while studying was higher at the start of Semester 1 2019 than at the start of Semester 2 2018. Give your response in one or two brief sentences.

Answer 1

a) Use the data to construct a 90% confidence interval for the population proportion of first year UC students who were working while studying at the start of Semester 1 2019.

b) Use the data to construct a 90% confidence interval for the population proportion of first year UC students who were working while studying at the start Semester 2 2018.

c) Use your confidence intervals to comment on the suggestion that the proportion of first-year UC students who were working while studying was higher at the start of Semester 1 2019 than at the start of Semester 2 2018. Give your response in one or two brief sentences.

53.36% to 59.88% were working at the start of Semester 1 2019.

Where 45.38% to 52.66% were working at the start of Semester 2 2018.

Hence we see that the proportion of first-year UC students who were working while studying was higher at the start of Semester 1 2019 than at the start of Semester 2 2018.