Matt Jones Math 1530 Elements of Statistics Exam III NAME Take the class period to complete this exam You may use a calculator a writing utensil one page of notes normal tables and your brain Do not share any materials and must do your own work to receive any credit Good luck 1 What are the necessary assumptions for making a t interval for a population mean 2 What are the necessary assumptions for performing a z test for a population mean 3 The average weight of cans of soup is reportedly 15 oz but you believe it might actually be more You would like to determine with some degree of certainty if the company is telling the truth You are a poor college student and can only afford twelve cans The weights in ounces of the contents of the twelve are below 15 11 15 05 15 03 14 95 15 08 15 05 15 01 14 99 15 03 15 02 15 00 15 01 a Are the necessary assumptions for performing a t test satisfied Explain Regardless of your answer to the previous part let s perform the test anyway if only just for practice b First write down the null and alternative hypotheses c Even for small samples from a NORMAL distribution if the company is telling the truth x 0 t0 s n has a t distribution with n 1 degrees of freedom Calculate t0 d What is the p value e Based on what you have done should you reject the company s claim or fail to reject the company s claim Explain 4 The average number of licks it took 40 people to get to the Tootsie Roll center of a Tootsie Pop was 1130 7 with a sample standard deviation of 65 a Are the assumptions for constructing a z interval satisfied b Are the assumptions for constructing a t interval satisfied c Based on your responses to the previous two questions construct a 95 confidence interval for the actual mean number of licks required Be sure to phrase your answer in a complete sentence as we have discussed in class 5 TRUE or FALSE A 96 confidence interval is one margin of error in width 6 TRUE or FALSE In theory 90 of all 90 confidence intervals will contain the population parameter of interest 7 The City of Clarksville wants you to make a 95 confidence interval for the average height of high school students The interval is to be no more than 2 inches in width From experience you believe the standard deviation of the heights to be 4 1 inches What is the minimum required number of students you must observe
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