# 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 c

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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.

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 c

(c) Using the information you obtained in part (b), check whether it is reasonable to assume that the two samples come from populations whose distributions have a common variance. [ 3] (d) To investigate whether light a ects root growth (when stems have been cut during growth), a t-test is to be performed on the measurements that you made. De ning and using appropriate notation, state the null and alternative hypotheses of this test. [ 2] (e) Use Minitab to perform the appropriate t-test on your data. (You should assume that the assumption of a common population variance is reasonable, regardless of the outcome of your investigation in part (c).) Include a copy of the relevant Minitab output in your answer. What is the result of the t-test? Carefully report your conclusions concerning the question of whether light a ects root growth of mustard seedlings. [ 6] (f ) A reservation about your conclusions in part (e), given the way in which the experiment was designed and carried out, might be that cutting the stems could have di erent e ects in the light and in the dark. Give two other valid reservations. [ 4] Question 2 (Unit 10) { 9 marks You should not use Minitab to answer this question, but 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. Table 2 Summary statistics for the battery life (in minutes) of a model of mobile phone Task Sample size Mean Standard deviation Web browsing 20 986 49 (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. [ 2] (b) What are the number of degrees of freedom and the 5% critical value for the most appropriate t-test applied to these data? [ 2] (c) Hence calculate a 95% con dence interval for the population mean battery life for this model of mobile phone, as measured during this task. [ 3] (d) Based on your calculated 95% con dence interval, is it plausible that the underlying population mean battery life is 1020 minutes as claimed by the manufacturer? Justify your answer. [ 2] page 3 of 5

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