A battery manufacturer claims its product lasts at least 5000 hours on average. A researcher carries out a hypothesis test to decide if the manufacturer's claim should be accepted or not. A sample of 80 batteries is tested. The average time before failure is 4900 hours, with a standard deviation of 500 hours. (a) State, in symbols or in words, the alternative hypothesis for testing the battery manufacturer's claim. [2 marks] (b) The results for this hypothesis test are given below. (i) What is the appropriate p-value? [1 mark] (ii) Is there evidence to reject the null? Explain. [1 mark] (iii) The researcher also estimated a 95% confidence interval for the mean battery life (in hours) of (4944,5056). Use this confidence interval along with the results of the hypothesis test to write a conclusion, in suitable language, for including in a report to the battery manufacturer. [2 marks] (c) Is it necessary to assume that battery lifetimes are normally distributed? Explain. [1 mark] A battery manufacturer claims its product lasts at least 5000 hours on average. A researcher carries out a hypothesis test to decide if the manufacturer's claim should be accepted or not. A sample of 80 batteries is tested. The average time before failure is 4900 hours, with a standard deviation of 500 hours. (a) State, in symbols or in words, the alternative hypothesis for testing the battery manufacturer's claim. [2 marks] (b) The results for this hypothesis test are given below. (i) What is the appropriate p-value? [1 mark] (ii) Is there evidence to reject the null? Explain. [1 mark] (iii) The researcher also estimated a 95% confidence interval for the mean battery life (in hours) of (4944,5056). Use this confidence interval along with the results of the hypothesis test to write a conclusion, in suitable language, for including in a report to the battery manufacturer. [2 marks] (c) Is it necessary to assume that battery lifetimes are normally distributed? Explain. [1 mark]