2018 EJC P2 Q8

A teacher, Mr. Ku, suspects that the average time a student spends on his or her mobile phone per day is \({{\mu }_{0}}\) minutes. He selected a random sample of \(97\) students in the school who own mobile phones and recorded the amount of time each student spent on his or her phone in a randomly selected day. The results are displayed in the table below.

1. Calculate unbiased estimates of the population mean and variance of the time a student spends on his or her mobile phone per day.[2]

The null hypothesis that the average time a student spends on his or her mobile phone per day is \({{\mu }_{0}}\) minutes is tested, at \(5\%\) level of significance, against the alternative hypothesis that the average time a student spends on his or her mobile phone per day differs from \({{\mu }_{0}}\) minutes.

2. Determine the range of values of \({{\mu }_{0}}\) for which the null hypothesis is rejected.[5]
3. Explain, in the context of this question, the meaning of ‘at \(5\%\) level of significance’.[1]
4. If the null hypothesis in (ii) is rejected at \(5\%\) significance level, can we reject the null hypothesis at \(1\%\) level of significance? Explain your answer.[1]