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Name: c) The company wants to have a product guarantee on its batteries that says something like, \"If our batteries last less than _ hours, then we'll replace it for free!" If the company only wishes to be responsible for replacing 7% of all the batteries they make, how many hours should they state in their guarantee? (4 pts) 8. Which of the following M describes the notion of a sampling distribution? (2 pts) a) It is any curve which has a total area of 1 below it. b) It describes the pattern of values that a statistic will take when repeated samples of size n are selected from the population. 0) It is used to nd the chances of obtaining certain values when an individual is selected from the population. d) It tells us how large a sample is needed in order for a statistic's distribution to exactly match the population's distribution. 9. Which of the following is the most ideal situation for a sampling distribution of a statistic? (2 pts) a) The statistic has high bias and low variability (\"standard error\"). b) The statistic has high bias and high variability (\"standard error\"). 6) The statistic has low bias and high variability (\"standard error\"). d) The statistic has low bias and low variability (\"standard error\"). 10. Which of the following is NOT true about the distribution of sample proportions (as we discovered in our lab work in which we ipped coins)? (2 pts) a) As the sample size increases, we see the pattern in the sample proportions more clearly. b) Sample proportions are said to be \"unbiased\" (or have bias = 0) since the center of the sampling distribution equals the population parameter. c) Sample proportions are distributed according to a uniform distribution. d) When discussing the sampling distribution for sample proportions, we as5ume that all samples collected are of the same size and are randomly selected. Spring 2021 page 6 of 10 Name: 11. Suppose there are over 3600 students currently registered at SUNY Adk. A question on a recent registration form determined that 30% all students believe that the \"no tobacco\" policy on campus should be reconsidered. We wish to select a random sample of 80 students and ask them their opinion on the \"no tobacco" policy. a) What are the conditions that must be met in order to use the normal distribution approximation to discuss this situation? Only state the conditions and move on to part b)! (3 pts) b) Are these conditions met in this situation? Show all work or gjve a brief explanation for each. (3 m) 0) Determine the mean and standard deviation for the normal distribution approximation in this situation. (3 pts) Spring 2021 page 7 of 10 Name: d) What is the probability that among our sample, we will find that more than 29% of people will be in favor of reconsidering the "no tobacco" policy? Sketch a picture of the information provided in this question. (4 pts) 12. If we keep the level of confidence fixed (say at 95%), which of the following will result in a "wider" confidence interval? (2 pts) a) Decreasing the sample size. b) Decreasing the population size. c) Increasing the sample size. d) Increasing the population size. 13. A researcher studies the cost of houses in a region and determines that the 95% confidence interval for the proportion of houses with a pool is 31.6%