1 Each working day, Beth takes a bus to her place of work. She believes that the mean time that her journey takes is 30 minutes. In order to check this, Beth selects a random sample of 8 journeys. The times in minutes for these 8 journeys are as follows.
\(\begin{array} { l l l l l l l l } 31.9 & 28.5 & 35.9 & 31.0 & 30.2 & 34.9 & 28.9 & 31.3 \end{array}\)
- What assumption does Beth need to make in order to construct a confidence interval for the mean journey time based on the \(t\) distribution?
- In this question you must show detailed reasoning.
Given that the assumption in part (a) is valid, determine a 95\% confidence interval for the mean journey time.
- Explain whether the confidence interval suggests that Beth may be correct in the belief that her mean journey time is 30 minutes.