Do the calculations ‘by hand’ (using a calculator), showing your working.

A manufacturer claims that a model of mobile phone has a battery life of 1020 minutes (i.e. 17 hours). In order to test this claim, 20 mobile phones of that model were fully charged and then used to perform a range of tasks. One task involved browsing the web continuously until the phones shut down. The length of time for each phone to shut down was recorded in minutes. The results are summarised in Table 2. – will provide the table 

(a) What is the most appropriate version of the t-test if you want to test the null hypothesis that the underlying population mean battery life for this model of phone is what the manufacturer claims it to be when the phone is used in this way? Justify your choice.

(b) What are the number of degrees of freedom and the 5% critical value for the most appropriate t-test applied to these data?

(c) Hence calculate a 95% confidence interval for the population mean battery life for this model of mobile phone, as measured during this task.

(d) Based on your calculated 95% confidence interval, is it plausible that the underlying population mean battery life is 1020 minutes as claimed by the manufacturer? Justify your answer.