Use the given statistics to complete parts (a) and (b). Assume that the populations are normally distributed. (a) Test whether u1 > H2 at the a = 0.01 level of significance for the given sample data. Population 1 Population 2 24 25 49.6 4.1 (b) Construct a 95% confidence interval about u1 - H2. 45.8 12.7 (a) Identify the null and alternative hypotheses for this test. B. Ho: H1 = H2 H1: H1>H2 O A. Ho: H1 = H2 O C. Ho: H1 + H2 H1: H1 = H2 H1: H1 #H2 O D. Ho: H1 H2 H1: H1 = H2 Find the test statistic for this hypothesis test. (Round to two decimal places as needed.)
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- You may need to use the appropriate appendix table or technology to answer this question. To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, a chemical company obtained the following data on the time (in minutes) need mix the material. Manufacturer 1 20 2 22 3 28 20 27 27 19 32 22 25 23 Use Fisher's LSD procedure to develop a 95% confidence interval estimate (in minutes) of the difference between the means for manufacturer 1 and manufacturer 2. (Round your answers to two decimal pla -677 x min to 4.77 Need Help? Road wwSample 2 Assume that both populations are normally distributed. a) Test whether µ, # µ, at the a = 0.05 level of significance for the given sample data. b) Construct a 95% confidence interval about u, - H2. Sample 1 17 13 17 14.3 3.5 3.1 E Click the icon to view the Student t-distribution table. A. Ho: H1 = H2, Hq: Hq # Hz O B. Ho: H1 = H2, H,: Hy H2 Determine the test statistic. t= - 1.15 (Round to two decimal places as needed.) Determine the critical value(s). Select the correct choice below and fill in the answer box(es) within your choice. (Round to three decimal places as needed.) O A. The critical value is O B. The lower critical value is -2.040. The upper critical value is 2.040. Should the hypothesis be rejected? Do not reject the null hypothesis because the test statistic is not in the critical region. b) Construct a 95% confidence interval about u, - H2. The confidence interval is the range from to| (Round to two decimal places as needed. Use ascending order.)Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find the bone density test scores that can be used as cutoff values separating the lowest 10% and highest 10%, indicating levels that are too low or too high, respectively. Sketch the region containing the lowest 10% and highest 10%. Choose the correct graph below. OA. -Za Za Q The bone density scores are ☐ OB. -Za Za (Use a comma to separate answers as needed. Round to two decimal places as needed.) ○ C. Q Za -Za D. Q a G Za -Za
- A study was conducted to measure the effectiveness of hypnotism in reducing pain. The measurements are centimete on a pain scale before and after hypnosis. Assume that the paired sample data are simple random samples and that th differences have a distribution that is approximately normal. Construct a 95% confidence interval for the mean of the "before - after" differences. Does hypnotism appear to be effective in reducing pain? Before After 4.8 6.3 2.4 2.6High-power experimental engines are being developed by the Stevens Motor Company for use in its new sports coupe. The engineers have calculated the maximum horsepower for the engine to be 810 HP. Sixteen engines are randomly selected for horsepower testing The sample has an average maximum HP of 890 with a standard deviation of 85 HP. Assume the population is normally distributed. Step 2 of 2: Use the confidence interval approach to determine whether the data suggest that the average maximum HP for the experimental engine is significantly different from the maximum horsepower calculated by the engineers. Answer D Tables Keypad Keyboard Shortcuts Because the hypothesized value does not fall in the interval, we fail to reject the null hypothesis. There is not sufficient evidence at the 0.01 significance level that the average maximum HP is different from the maximum HP calculated by the engineers. Because the hypothesized value falls in the interval, we reject the null hypothesis. There…Having done poorly on a particular exam in a junior high school, 24 students decide to write the exam again to try and improve their mark. Results are given in the following table. ITT Student Attempt 1 (A1) Attempt 2 (A2) Difference (d= A1 - A2) Average Standard deviation 24 55 3.0 24 58 4.4 24 -3.0 2.4 (a) Find an 80% confidence interval for the difference in mean scores between attempt 1 and attempt 2. (Round your answers to 4 decimal places, if needed.) (b) Based on this confidence interval, can we conclude there is a difference in mean scores between attempt 1 and attempt 2? O Yes, since the interval is completely below 0. O No, since the interval contains 0. O Yes, since the interval contains 0. O No, since the interval is completely below 0.Create a 90% confidence interval for the data set below. 53 62 62 58 60 61 70 53 70 59 61 60 ( , ) [three decimal accuracy] [three decimal accuracy]1) Treatment group Placebo group n₁ = 50 n2=100 x1 = 7.00 $1 = 1.00 x2 = 6.00 $2 = 2.00 Test the claim that the two samples come from populations with the same mean. Use a = .05. Draw it: Conclusion (full sentence): Ho= HA= Calculated value p-value Decision Find the 95% confidence interval for the difference between the two population means to the nearest hundredth.3. A company wants to test a new energy drink. Two groups of samples were pooled out from the population. Find a 95% confidence interval for the difference between the two population means using the provided information below: Group Sample Size Standard Deviation Sample Mean (100-m running speed in seconds) Group A 45 125 10 Group B 60 140 8How do you solve this problem?Test the claim that the proportion of people who own cats is significantly different than 80% at the 0.1 significance level.The null and alternative hypothesis would be: H0:μ=0.8H0:μ=0.8H1:μ≠0.8H1:μ≠0.8 H0:p=0.8H0:p=0.8H1:p≠0.8H1:p≠0.8 H0:p≤0.8H0:p≤0.8H1:p>0.8H1:p>0.8 H0:p≥0.8H0:p≥0.8H1:p<0.8H1:p<0.8 H0:μ≤0.8H0:μ≤0.8H1:μ>0.8H1:μ>0.8 H0:μ≥0.8H0:μ≥0.8H1:μ<0.8H1:μ<0.8 The test is: right-tailed left-tailed two-tailed Based on a sample of 200 people, 87% owned catsThe p-value is: (to 2 decimals)Based on this we: Reject the null hypothesis Fail to reject the null hypothesisThe data below are yields for two different types of corn seed that were used on adjacent plots of land. Assume that the data are simple random samples and that the differences have a distribution that is approximately normal. Construct a 95% confidence interval estimate of the difference between type 1 and type 2 yields. What does the confidence interval suggest about farmer Joe's claim that type 1 seed is better than type 2 seed? Турe 1 Туpe 2 2054 1956 2067 2540 2213 1977 2254 1544 2038 1992 2072 2477 2126 1926 2137 1442 In this example, µg is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the type 1 seed yield minus the type 2 seed yield. The 95% confidence interval isSEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. 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