not accept your exam afterwa ptions. Good luck! 1. Suppose that X ~ N(0,2). (a) What is the probability that X is less that -2? (b) What is the probability that X is between 1 and 2? (c) What is the probability that X is exactly 3? (d) What value corresponds to the second decile (20th percentile)? 2. A variable is normally distributed with mean 0 and standard deviation 8. (a) Determine the quartiles for this random variable. (b) Find the 40th percentile. (c) Find the value associated with the bottom 10% of the data. 3. Scores on the SAT verbal are approximately normally distributed with mean 500 and standard deviation of 100. (a) What is the probability that a randomly selected student scored more that 650 on the SAT? (b) What is the probability that a randomly selected student scored a score between 450 and 600? (c) If 20 students are randomly selected, what is the probability that the mean SAT score will be more that 670? Be sure that requirements satisfy. (d) What mean score is associated with the highest 10%? 4. 78% of all people who smoke tend to suffer from lung cancer in the long run. We sample 100 smokers and find that 58 of them suffer from lung cancer. Has the proportion of people who smoke and suffer from lung cancer changed? Use 0.05 significance to test this. 5. Suppose that the heights of all males are normally distributed with mean 69.5 in. and standard deviation 2.4 in. (a) What is the probability that a randomly selected individual will have a height that is more than 72 in? (b) What height is associated with Q3, the third quartile? (c) Suppose we sampled 10 males. What is the probability that the mean height is less than 75 in? (d) What mean score is associated with the highest 5%? 6. Determine whether the following statements are true or false. If they are false, explain why. (a) Increasing the level of confidence will decrease the width of the confidence interval. (b) If you have a two-tailed hypothesis test, the p-value must be multiplied by 2. (C) If the test statistic falls into the critical region, then we fail to reject the null hypothesis. (d) If our confidence interval for u was (482.4,490.7) with 95% confidence, then that means that 95% of all sample means will fall between 482.4 and 490.7. (e) Suppose that we constructed a hypothesis test and got a p-value of 0. If our significance level is 0.01, then we reject the null hypothesis. (f) If we test a claim about the population mean and the standard deviation is un- known, then the test will be a z-test with n - 1 degrees of freedom. 7. A botanist claims that the mean concentration of glucose in a plant's stem is about 0.3 M. As a result, a young researcher determines the molarity of 35 stems and discovers that they had a mean of 0.27 M with a standard deviation of 2.4 M. Based on these results, does it appear that the mean concentration of glucose has changed? Use a 0.01 significance level to test this. 8. A flare in break dancing is when the legs of a person move in a circle around the body without touching the ground. It is known that the average height at which a dancer can perform a flare in the air is 3.2 ft. In order to test this, we randomly selected 87 novice dancers to perform the flare and found that the mean height was 2.7 ft. Use 0.05 significance to test the claim that the mean height of break dancers who can successfully perform the flare on the first try is less that 3.2. Assume that the population standard deviation is 1.8 ft and be sure to check assumptions. 9. We are interested in identifying the mean weight of an adult brain. To do this, we weigh 48 brains and find that the mean weight was 3.4 lb with a standard deviation of 4.2. (a) Construct a 90% confidence interval estimate for the mean weight of an adult brain and interpret it Use the appropriate confidence interval. (b) Suppose now that the population standard deviation is known to be 3.7. Construct the 90% confidence interval estimate with this new piece of information. (C) How many samples must we take so that we can be 99% confident that the sample percentage is in error by no more than 0.3 brains? Use the value of o in part (b). Page 2
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