2025 JPJC P2 Q6

A particular streaming service platform claims that the average time a user spends watching content on the platform per visit is more than \(15\) minutes. A team of data analysts for the platform wants to verify this claim. They randomly select a sample of \(80\) users and record the amount of time each user spends watching content in a single visit. The sample mean of time spent is found to be \(16\) minutes. The population standard deviation of time spent is assumed to be \(\sigma\) minutes.

1. Explain why the team should carry out a \(1\)-tail test.[1]

A test at the \(5\%\) significance level indicates that the platform's claim is valid.

2. Explain why the team is able to carry out a hypothesis test without knowing anything about the distribution of the times spent by the users.[1]
3. Find the range of values of \(\sigma\).[4]
4. Explain, in the context of the question, the meaning of 'at the \(5\%\) significance level'.[1]