Exercise 1: What are the different ways to conduct inferential statistics? Provide a summary of each of them.

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please help with question 1, question 2 a and question 2 b

Exercise 1: What are the different ways to conduct inferential statistics? Provide a summary of
each of them.
Exercise 2: Solve the following:
2.1 Use case 1: The manufacturer of a certain brand of auto batteries claims that the mean life of these
batteries is 45 months. A consumer protection agency that wants to check this claim took a random sample
of 24 such batteries and found that the mean life for this sample is 43.05 months. The lives of all such
batteries have a normal distribution with the population standard deviation of 4.5 months.
a. Find the p-value for the test of hypothesis with the alternative hypothesis that the mean life of these
batteries is less than 45 months. Will you reject the null hypothesis at a = .025?
b. Test the hypothesis of part a using the critical-value approach and a = .025.
2.2 Use case 2: A consumer organization tested two paper shredders, the Piranha and the Crocodile,
designed for home use. Each of 10 randomly selected volunteers shredded 100 sheets of paper with the
Piranha, and then another sample of 10 randomly selected volunteers each shredded 100 sheets with the
Crocodile. The Piranha took an average of 203 seconds to shred 100 sheets with a standard deviation of 6
seconds. The Crocodile took an average of 187 seconds to shred 100 sheets with a standard deviation of 5
seconds. Assume that the shredding times for both machines are approximately normally distributed with
equal but unknown standard deviations.
a. Construct a 99% confidence interval for the difference between the two population means.
b. Using a 1% significance level, can you conclude that the mean time taken by the Piranha to shred 100
sheets is higher than that for the Crocodile?
c. What would your decision be in part b if the probability of making a Type I error were zero? Explain.
Transcribed Image Text:Exercise 1: What are the different ways to conduct inferential statistics? Provide a summary of each of them. Exercise 2: Solve the following: 2.1 Use case 1: The manufacturer of a certain brand of auto batteries claims that the mean life of these batteries is 45 months. A consumer protection agency that wants to check this claim took a random sample of 24 such batteries and found that the mean life for this sample is 43.05 months. The lives of all such batteries have a normal distribution with the population standard deviation of 4.5 months. a. Find the p-value for the test of hypothesis with the alternative hypothesis that the mean life of these batteries is less than 45 months. Will you reject the null hypothesis at a = .025? b. Test the hypothesis of part a using the critical-value approach and a = .025. 2.2 Use case 2: A consumer organization tested two paper shredders, the Piranha and the Crocodile, designed for home use. Each of 10 randomly selected volunteers shredded 100 sheets of paper with the Piranha, and then another sample of 10 randomly selected volunteers each shredded 100 sheets with the Crocodile. The Piranha took an average of 203 seconds to shred 100 sheets with a standard deviation of 6 seconds. The Crocodile took an average of 187 seconds to shred 100 sheets with a standard deviation of 5 seconds. Assume that the shredding times for both machines are approximately normally distributed with equal but unknown standard deviations. a. Construct a 99% confidence interval for the difference between the two population means. b. Using a 1% significance level, can you conclude that the mean time taken by the Piranha to shred 100 sheets is higher than that for the Crocodile? c. What would your decision be in part b if the probability of making a Type I error were zero? Explain.
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