Lindsey D. Bell Math 1040 Tiffany Hilton Term Project Part 6- Hypothesis Testing Part 6: Hypothesis Tests (1% of course grade) Explain in general the purpose and meaning of a hypothesis test. Answer: A hypothesis test is the procedure used to test a claim about a property of a population, meaning: when given a claim about a certain population, we can use the hypothesis test to determine if the claim is true or not, whether to reject or fail to reject the claim, if there is sufficient or insufficient evidence relevant to the claim and be able to state the conclusion about the claim in simple and nontechnical terms. Red 9 13 10 13 14 9 14 12 15 7 10 13 7 14 15 9 19 13 15 9 14 11 9 10 20 15 7 Lindsey D. Bell Math 1040 Tiffany Hilton Term Project Part 6- Hypothesis Testing Using values for the class data that you computed in Part 3 of the project and a 0.05 significance level, test the claim that 20% of all Skittles candies are red. Show all the steps (neatly written and scanned or typed). Discuss and interpret the results. Answer: Class Total of Red Skittles = 326 p: proportion of skittles that are red (class population) H0: p=0.20, H1: p≠0.20 x= 326, n= 27, p= 0.20, p-hat (x/n) = 326/27= 12.074, q (1-n) = 1-0.20= 0.80 z= p-hat-p/sqrt (p*q/n) z= (326/27)-0.20/ sqrt ((0.20) (0.80)/326) = 3.05 z= 0.9989 p-value = 1-0.9989= 0.0011 *Since 0.0011 <0.05 (significance level) we reject the null hypothesis; we reject the null hypothesis that 0.20 of Skittles candies in a regular sized bag are red candies. Using values for the class data that you computed in Part 4 of the project and a 0.01 significance level, test the claim that the mean number of candies in a bag of Skittles more than 55. Show all the steps H0: p> 55 H1: p< 55 n= 27, x-bar = 12.07407407, n= 27, s= 3.40729902, df= 26 t= x-bar – mu x-bar/s/sqrt n t= 12.07407407-55/3.40729902/sqrt (27) = -65.462 t=2.479 Lindsey D. Bell Math 1040 Tiffany Hilton Term Project Part 6- Hypothesis Testing List the requirements for doing each of the two hypothesis tests you performed (see pages 400 and 412 in the textbook). Discuss whether or not your samples met each of these requirements. Hint: use the sampling method from Part 2 of the project to answer part of this. (15 points) Answer: Testing a claim about a population proportion Requirements: - - The sample observations are simple random sample The conditions for a binomial distribution are satisfied. (There are a fixed number of independent trials having constant probabilities, and each trial has two outcome categories of “success” and “failure.”) The conditions np > 5 and nq > 5 are both satisfied, so the binomial distribution of sample proportions can be approximated by a normal distribution with mu = np and population standard deviation = sqrt (n*p*q). Testing a claim about a population mean (with population standard deviation not known) - The sample is a simple random sample Either or both of these conditions is satisfied: the population is normally distributed or n > 30
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