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Nutrition labels. The nutrition label on a bag of potato chips says that a serving of potato chips has 130 calories. You believe this is incorrect and take a random sample of 49 bags that yielded a sample mean of 134 calories with a standard deviation of 13" calories. Test the claim at a 533 level of significance that the number of calories Listed on the nutrition label on a bag of potato chips is not correct. {a} Write the hypotheses for the test: {b} l[Zompute the p-value for the test: p = (round to three sfg figs} (2 What is the final conclusion? (:3 There is not sufficient evidence to reject the claim that the true average calorie content is different from 130 calories. C?) There is not sufficient evidence to support the claim that the true average calorie content is different from 130 calories. 0 There is sufficient evidence to support the claim that the true average calorie content is different from 130 calories. (:3 There is sufficient evidence to reject the claim that the true average calorie content is different from 130 calories. Test Prep. A GRE prep company advertises that average score improvement in GRE scores of their students is equal to EU points. A consumer group believes this is incorrect and randomly samples 35 students who have taken the GRE prep course from this company. They find that the sample has an average improvement of 36 points with a standard deviation of 3? points. Evaluate the consumer groups belief that the company's advertised score improvement is incorrect. Use a 55%. level of significance. [a] 1Write the hypotheses for the test: {b} Compute the p-value for the test: p = (round to four decimal places} c What is the final conclusion? (i) There is sufficient evidence to support the average score increase in GRE is not 50 points. (:3 There is not sufficient evidence to support the average score increase in GRE is not 50 points. (:3 There is sufficient evidence to reject the average score increase in GRE is not 50 points. (:3 There is not sufficient evidence to reject the average score increase in GRE is not 50 points. Fresh Donuts! Adonut company claims that their donuts remain fresh for more than 2 days on average. A donut watchdog organization samples 12 donuE and finds that on average they remain fresh 2.6 days with a standard deviation of 1.1 days. Evaluate the company's claim using a hypothesis test. Use a 57-3\" level of significance. Assume that donut freshness follows a normal distribution. {a] Write the hypotheses for the test: (2) Ho: p = 2.5 Ha: p = 2.15 (2) HO: p = 2.5 Ha: p 2.15 (i) HO: p = 2 Ha: p > 2 C'Ho:p=2 Ha:p=2 {b} Compute the p-value for the test: p = (round to four decimal places) c What is the final conclusion? C) There is not sufficient evidence to support the company's claim. C) There is not sufficient evidence to reject the company's claim. Q) There is sufficient evidence to support the company's claim. C) There is sufficient evidence to reject the company's claim. You wish to test the following claim {H5} at a significance level of CI: = Ill. Hp:p=l}.1 Ha:pal].1 You believe the population is normally distributed, but you do not know the standard deviation. a. What is the test statistic for this sample? test statistic = I I Round to 3 decimal places b. What is the p-ualue for this sample? p-value = I I Round to 4 decimal places. c. The nvalue is... (El less than [or equal to] a CI greater than ct do v" d. This test statistic leads to a decision to... (i) reject the null Cl accept the null CI fail to reject the null do u\" e. As such the final conclusion is that... C] There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 6111. C) There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 150.1. (E) The sample data support the claim that the population mean is not equal to 60.1. (:3 There is not sufficient sample evidence to support the claim that the population mean is not equal to 60.1. cgv" Test Prep. A GRE prep company has indicated that the average score improvement of their students is equal to 70 points. We claim they are incorrect, and want to test to see if the average score improvement is different than 70. We randomly sample students for their average improvement. The data we collected are below. GRE scores are known to be normally distributed. Points 73.1 42.5 62.1 73.9 58.9 57.6 67.5 53.4 64 58.6 61.2 Evaluate the company's claim using a hypothesis test. You wish to test the following claim (Ha) at a significance level of or = 0.05. (a) Write the hypothesis for the test. OH: H = 70 Ha: H = 70 OH: H = 70 Ha: H 70 OH: H = 61.164 Ha: H = 61.164 OH: H = 61.164 Ha: p 61.164 (b) What is the P-value for this test (round to 4 decimal place)(c) Based on the sample data, we sould conclude that ... O There is enough evidence at the o = 0.05 level to say that the average improvement is not 70 points. There is not enough evidence at the o = 0.05 level to say that the average improvement is not 70.Fresh Donuts! A donut company says that their donuts remain fresh for over 3 days on average. We tested a random sample of donuts for how long they remained fresh. The data are below. Assume donut freshness is normally distributed. days 3.3 3.3 4.5 4.2 3.5 3.1 4. 1 3 4.2 4.6 3.9 2.5 4.1 3.9 2.6 3.6 3.3 2.9 Evaluate the company's claim using a hypothesis test. (a) Write the hypothesis for the test. OH,: H = 3 Ha: H = 3 OH: H = 3 Ha: H 3 OH: H = 3.611 Ha: H = 3.611 OH: H = 3.611 Ha: H 3.611{b} What is the pvalue for this test? {round to 4 decimal places} c Based on the samlle data we should conclude that There is sufficient evidence at the cc = {ID-5 Level to say that the average donut stays fresh fcur more than 3 days. [:1 There is not sufficient evidence at the ct = [L05 level to say that the average donut stays fresh fer more than 3 days. div\" The Average Work Week Kara, a newly hired engineer, has been informed that the mean work week for engineers in start-up companies is 55 hours. Kara hopes that the mean hours worked per week is less than 55 hours. She asks random engineers in start-ups for the lengths of their mean work weeks. The data are below. Assume work time is normally distributed. Hours 16 42 42 47 55 33 54 53 45 68 57 39 37 31 68 43 40 59 59 50 51 62 43 54 36 Evaluate Kara's claim using a hypothesis test.Write the hypothesis for the test. OH: H = 55 Ha: H = 55 OH: H = 55 Ha: H 55 OH: H = 48.56 Ha: H = 48.56 OH: H = 48.56 Ha: H 48.56 What is the p-value of this test? (round to 4 places Based on the sample data, we should conclude that ... There is sufficient evidence at the o = 0.05 level that the average work week is less that 55 hours. There is not sufficient evidence at the o = 0.05 level that the average work week is less that 55 hours