Math 150, Spring 202.1 El Gemini: College G. Song Chapter 8: Worksheet Section 8.1: Basics of Hypothesis Testing 1: Denitions: a: What is the null hypothesis? What is the symbol for null hypothesis? b: What is the alternative hypothesis? \"That is the symbol for alterna tive hypothesis? c: What are some commonly used test statistics [symbols]? d: What is the critical region [or rejection region}? e: What are the P-value and the critical values? What are we com paring the P-value to? What are we comparing the critical values to? Section 8.2: Testing a Claim About a Proportion Note: I have also include the nal answers for the test statistics and the poolues for each problem ows #2 to #11 so that you can compare your answer. 2: A genetic experiment involving peas yielded one sample of offspring consisting of 403 green peas and 126 yellow peas. Use a 0.05 signicance level to test the claim that under the same circumstances, 35% of offspring peas will be yellow. Identify the null hypothesis, alternative hypothesis, test statistic, Pvalue, conclusion about the null hypothesis, and nal conclusion that addresses the original claim. Use the Pvalue method and the normal distribution as an approximation to the binomial distribution. test statistic = 5.391830269, pvalue = 0.000000136990094 3: A dearold girl did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy eld. She ipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under her hand without seeing it and without touching it. Among 288 trials, the touch therapists were correct 12? times. Use a 0.01 signicance level to test the claim that touch therapists use a method equivalent to random guesses. test statistic = 2.003469213, pvalue = 00451268092 Math 150: SE' 5 2021 El Camino Collegg G. Song 4: Consider a sample of 50 football games, where 2'." of them were won by the home team. Use a 0.10 signicance level to test the claim that the probability that the home team wins is greater than onehalf. test statistic 2 05658854249, pvalue 2 02858037831 Suppose that in a random selection of 100 colored candies, 21% of them are blue. The candy company claims that the percentage of blue candies is equal to 30%. Use a 0.05 signicance level to test that claim. test statistic = 1.963961012, pvalue = 0495344733 In a certain survey, 520 people chose to respond to this question: \"Should passwords be replaced with biometric security (ngerprints, etc)?\" Among the respondents, 52% said \"yes." We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security. test statistic = 09121403401, pvalue = 018088473933 Section 8.3: Testing a Claim about a Mean A data set about a smartphone carrier's data speeds at airports is given and the summary statistics are n = 50,5 = 5.32, a = 1.34. Use a 0.05 signicance level to test the claim that the data are from a population having a mean less than 6.00 Mbps. Identify the null and alternative hypothesis, test statistics, Pvalue, and state the nal conclusion that addresses the original claim. test statistic = 3.588303089, pvalue = 000038370584 In a test of the effectiveness of garlic for lowering cholesterol, 64 subjects (assume that this is a simple random sample) were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes (before minus after) in their levels of LDL cholesterol (in mgf'dl) have a mean of 0.8 and a standard deviation of 21.2. Use a 0.05 signicance level to test the claim that with garlic treatment, the mean change in LDL cholesterol is greater than 0. Identify the null and alternative hypothesis, test statistics, Pvalue, and state the nal conclusion that addresses the original claim. test statistic = 03018887925, pvalue = 03818663481 Math 150, Spring 2021 El Camino College G. Song 9: A group of students estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below: 77, 92, 45, 71, 52, 31, 67, 74, 77, 56, 73, 81, 99, 96, 77 Use a 0.01 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Identify the null and alternative hypothesis, test statistics, P-value, and state the final conclusion that addresses the original claim. test statistic = 2.307253274, p-value = 0.0368399104 10: A safety administration conducted crash tests of child booster seats for cars. Listed below are results from those test, with the measurements given in hic (standard head injury condition units). 671, 745, 1195, 629, 601, 575 The safety requirement is that the hic measurement should be less than 1000 hic. use a 0.05 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. Assume that a simple random sample has been selected from a normally distributed population. Identify the null and alternative hypothesis, test statistics, P-value, and state the final conclusion that addresses the original claim. test statistic = -2.779809936, p-value = 0.0194554161 11: Use the pulse rates in beasts per minute (bmp) of a random sample of adult females listed in the data set below to test the claim that the mean is great than 68 bpm. 98 48 75 48 76 76 44 88 64 71 80 96 65 87 64 55 52 48 71 97 56 80 48 81 98 72 92 97 70 48 48 82 66 66 69 98 91 61 92 82 Use a 0.10 significance level. Identify the null and alternative hypothesis, test statistics, P-value, and state the final conclusion that addresses the original claim. test statistic = 1.656962303, p-value = 0.0527758072