Exercise 6.2: On the use of the standard deviation, we have discussed the empirical rule for a bell-shaped curve. By using the standard normal distribution table, verify the validity of the empirical rule.
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- Español A coin-operated drink machine was designed to discharge a mean of 7 fluid ounces of coffee per cup. In a test of the machine, the discharge amounts in 14 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 7.08 fluid ounces and 0.25 fluid ounces, respectively. If we assume that the discharge amounts are approximately normally distributed, is there enough evidence, to conclude that the population mean discharge, u, differs from 7 fluid ounces? Use the 0.10 level of significance. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H. Ho :0 H :0 (b) Determine the type of test statistic to use. O=0 OSO (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) OThe mean score on a driving exam for a group of driver’s education students is 76 points, with a standard deviation of 6 points. Apply chebychev’s theorem to the data using K=2. Interpret, At least ___% of the exam score falls between ___and ____carbon monoxide in the air in U.S. cities is less than 2.32 parts per million. It was found that the mean amount Test a claim that the mean amount e standard deviation is 2.12 parts per million. At a = 0.05, can the claim be supported? Complete parts (a) through (e) below. Assume the population is normally distributed. carbon monoxide in the air for the random sample of 64 cities is 2.41 parts per million and the (a) Identify the claim and state Ho and H. Which of the following correctly states Ho and H? AA :°H "H (Type integers or decimals. Do not round.) The claim is the V hypothesis. (b) Use technology to find the critical value(s) and identify the rejection region(s). The critical value(s) is/are to =U- (Use a comma to separate answers as needed. Round to two decimal places as needed.) Choose the graph which shows the rejection region. O B. "a O of (c) Find the standardized test statistic, t. The standardized test statistic is t=- (Round to two decimal nlaces as neadedHow do you find (b.)?IQ scores among the general population have a mean of 100 and a standard deviation of 14. A researcher claims that the standard deviation, o, of IQ scores for females is not equal to 14. A random sample of 24 IQ scores females had a mean of 98 and a standard deviation of 11. Assuming that IQ scores for females are approximately normally distributed, is there significant evidence (at the 0.05 level of significance) to conclude that the researcher's claim is correct? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. H, :0 H, :0 (b) Determine the type of test statistic to use. (Choose one) ▼ O=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) O1A random sample of n1 = 49 measurements from a population with population standard deviation ?1 = 3 had a sample mean of x1 = 10. An independent random sample of n2 = 64 measurements from a second population with population standard deviation ?2 = 4 had a sample mean of x2 = 12. Test the claim that the population means are different. Use level of significance 0.01. (a) Check Requirements: What distribution does the sample test statistic follow? Explain. The Student's t. We assume that both population distributions are approximately normal with known standard deviations.The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. (b) State the hypotheses. H0: ?1 = ?2;…"A fitness coach woud like to determine whether her aerobic fitness intervention leads to a significant increase or decrease in the one rep max (i.e., heaviest possible weight that can be lifted once) for deadlifts in her group of athletes (n = 13). She finds that the mean difference = 3 lbs, with a sum of squared deviation (SS) = 84. Calculate the t-statistic the fitness coach would observe given this data. (Be sure to round your answer to the second decimal place)."Arandom sample of 77 eighth grade students scores on a national mathematics assessment test has a mean score of 266. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 260. Assume that the population standard deviation is 37. At a= 0.13, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify Hg and H,. Choose the correct answer below. OB. Hg u 260 D. Họ: us 260 H, > 260 (claim) O. H: u= 260 (claim) H, u> 260 OF. H: pa 260 (claim) H, p 260 (claim) (b) Find the standardized test statistic z, and ts corresponding area 2= 1.42 (Round to two decimal places as needed) (c) Find the P-value. Pvalue =D(Round to three decimal places as needed.)(b) A mileage test is conducted for a new car model, the "HERO". In previous test, the population mean is 27 miles per gallon (mpg). Twenty-eight random selected Heros are driven for a month and the mileage is carefully measured in each. The mean mileage for the sample is =28.6mpg and the sample standard deviation is s = 2.2 mpg. Assuming 1-distribution is followed, answer the following questions. Hypothesis are given as follows: (i) H₁:μ=27 H: μ = 27 Find the degree of freedom of the test. By using 10% level of significance, find the critical value and show the rejection area. (iii) Calculate the test statistic, 1, to test the Ho. (iv) Determine whether you reject Ho. State your reason and conclusion. liA random sample of 75 eighth grade students' scores on a national mathematics assessment test has a mean score of 278. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 270. Assume that the population standard deviation is 34. At a = 0.15, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify Ho and Ha. Choose the correct answer below. O C. Ho: µ2 270 (claim) Ha: H 270 O F. Ho: H= 270 Ha: H> 270 (claim) O E. Ho: us270 O D. Ho: H= 270 (claim) Ha: H> 270 Ha: µ> 270 (claim) (b) Find the standardized test statistic z, and its corresponding area. (Round to two decimal places as needed.) (c) Find the P-value. P-value = (Round to three decimal places as needed.)Can you please check my workSEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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