Hypothesis Testing: A restaurant says that its hamburgers have 10 grams of fat. You work for a nutritional health agency and are asked to test this whether they actually have more than this. You find that a random sample of 9 hamburgers has a mean fat content of 13.5 grams and a standard deviation of s= 5.8 grams. At α= 0.10, do you have enough evidence to reject the restaurant’s claim?
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Hypothesis Testing:
A restaurant says that its hamburgers have 10 grams of fat. You work for a nutritional health agency and are asked to test this whether they actually have more than this. You find that a random sample of 9 hamburgers has a
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- Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value t,/2, (b) find the critical value z/2, or (c) state that neither the normal 40- distribution nor the t distribution applies. 30- The confidence level is 95%, o is not known, and the histogram of 58 player salaries (in thousands of dollars) of football players on a team is as shown. 20- 10- 0- 4000 Salary (thousands of dollars) 8000 12000 16000 20000 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. ta/2 = %3D (Round to two decimal places as needed.) В. Za/2 =| (Round to two decimal places as needed.) O C. Neither the normal distribution nor the t distribution applies. FrequencyYou are testing the claim that the mean GPA of night students is different from the mean GPA of day students. You sample 20 night students, and the sample mean GPA is 2.85 with a standard deviation of 0.86. You sample 30 day students, and the sample mean GPA is 3.02 with a standard deviation of 0.4. Test the claim using a 5% level of significance. Assume the population standard deviations are unequal and that GPAs are normally distributed. Give answer to at least 4 decimal places. What are the correct hypotheses?H0: = H1: Based on the hypotheses, find the following:Test Statistic = p− value = The correct decision is to The correct summary would be: that the mean GPA of night students is different from the mean GPA of day students.Use z scores to compare the given values. The tallest living man at one time had a height of 238 cm. The shortest living man at that time had a height of 142.4 cm. Heights of men at that time had a mean of 175.45 cm and a standard deviation of 5.59 cm. Which of these two men had the height that was more extreme? ... Since the z score for the tallest man is z = 0 and the z score for the shortest man is z = the man had the height that was Im- more extreme. (Round to two decimal places.) shortest tallest
- You are testing the claim that the mean GPA of night students is different from the mean GPA of day students. You sample 20 night students, and the sample mean GPA is 2.94 with a standard deviation of 0.8. You sample 55 day students, and the sample mean GPA is 2.56 with a standard deviation of 0.44. Test the claim using a 1% level of significance. Assume the population standard deviations are unequal and that GPAs are normally distributed. What are the correct hypotheses? Based on the hypotheses, find the following:Test Statistic = Critical Values = ±Are you smarter than a second-grader? A random sample of 59 second-graders in a certain school district are given a standardized mathematics skills test. The sample mean score is X=56. Assume the standard deviation of test scores is o= 15. The nationwide average score on this test is 50. The school superintendent wants to know whether the second-graders in her school district have greater math skills than the nationwide average. Use the a = 0.05 level of significance and the P-value method with the TI-84 calculator. Answer the following questions.You are testing the claim that the mean GPA of night students is different from the mean GPA of day students. You sample 35 night students, and the sample mean GPA is 2.91 with a standard deviation of 0.97. You sample 20 day students, and the sample mean GPA is 2.99 with a standard deviation of 0.82. Test the claim using a 1% level of significance. Assume the population standard deviations are unequal and that GPAS are normally distributed. Give answer to at least 4 decimal places. What are the correct hypotheses? Ho: M₁ H₁: M₁ Test Statistic = Critical Values = = ± H₁₂ Based on the hypotheses, find the following: ≠v H₂ OF (Just enter the positive CV.) The correct decision is to Fail to reject the null hypothesis The correct summary would be: There is not enough evidence to support the claim ✓ of night students is different from the mean GPA of day students. o that the mean GPA
- You suspect that people living in urban areas produce on average more garbage (X)than those living in rural areas (Y). To verify this opinion, you draw two samples and collect information on the amount of garbage produced in a month (measured in kilos). The first sample, made of 8 subjects living in an urban area, provides a sample mean equal to 40.5 and a sample standard deviation equal to 5.6; in the second sample, made of 10 subjects living in rural areas, the sample mean is 35.6 and the sample standard deviation is 7.5. It is assumed that the two populations are normal with the same unknown variance.Test the null hypothesis that the two population means are equal against a one-sided alternative according to which people living in urban areas produce on average more garbage than those living in rural areas. Use a 1% significance level.You are testing the claim that the mean GPA of night students is different from the mean GPA of day students. You sample 60 night students, and the sample mean GPA is 2.83 with a standard deviation of 0.52. You sample 50 day students, and the sample mean GPA is 3.21 with a standard deviation of 0.65. Test the claim using a 1% level of significance. Assume the population standard deviations are unequal and that GPAS are normally distributed. Give answer to at least 4 decimal places. What are the correct hypotheses? Ho: (H, H, H1: [H, Based on the hypotheses, find the following: Test Statistic = -3.3161 Critical Values = +2.576 X (Just enter the positive CV.)Are you smarter than a second-grader? A random sample of 57 second-graders in a certain school district are given a standardized mathematics skills test. The sample mean score is x =46. Assume the standard deviation of test scores is o = 15. The nationwide average score on this test is 50. The school superintendent wants to know whether the second-graders in her school district have weaker math skills than the nationwide average. Use the a=0.05 level of significance and the P-value method with the TI-84 calculator. Part: 0/ 4 Part 1 of 4 State the appropriate null and alternate hypotheses. H: OAfter 84 students at a particular university take a psychological evaluation, the sample mean score on the test is calculated to be 117 with a standard deviation of 44. We are interested in testing whether or not the mean score of the students at this university is different than the published population average of 112. Calculate the value of the test statistic and then use that to determine the appropriate p-value. 0.5952 0.2976 0.1488 0.8512 1.7024 0.1488 0.0744E= Over the years, the mean customer satisfaction rating at a local restaurant has been 65. The restaurant was recently remodeled, and now the management claims the mean customer rating, u, is not equal to 65. In a sample of 32 customers chosen at random, the mean customer rating is 76.2. Assume that the population standard deviation of customer ratings is 22.8. Is there enough evidence to support the claim that the mean customer rating is different from 65? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis H, and the alternative hypothesis H,. Ho Aa OA clinical study was conducted on a medicine and the data obtained as follows: calculate Sensitivity Diseased •True Positive: 1000 •True negative: 50 Non diseased •True positive: 100 •True negative: 800Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. 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