The following data are the joint temperatures of the O-rings (°F) for each test firing or actual launch of the space shuttle rocket motor (from Presidential Commission on the Space Shuttle Challenger Accident, Vol. 1, pp. 129-131): 83 49 61 40 83 67 45 66 70 69 80 58 68 60 67 72 73 70 57 63 70 78 52 67 53 67 75 Round your answers to 2 decimal places (e.g. 98.76). (a) Using the entire data, calculate the sample mean and sample standard deviation. Sample mean = 65.83 Sample standard deviation = (b) Remove the smallest observation (31°F) and calculate the sample mean and sample standard deviation of the remaining data. Sample mean Sample standard deviation-
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- Obtain the Z scores on each subject’s age. DATA Subject Gender Marital Status Age Education Household Income Personal Income 1 F 1 30 0 70000.00 40000.00 2 F 0 40 0 32500.00 32500.00 3 M 1 45 0 42000.00 .0 4 M 1 23 0 50000.00 50000.00 5 M 0 50 0 4500.00 4500.00 6 F 0 65 1 40000.00 22000.00 7 F 1 33 1 12000.00 12000.00 8 F 0 20 2 56000.00 52000.00 9 F missing 30 3 17500.00 17500.00 10 M 1 Missing 4 44000.00 39000.00 11 M 2 58 1 missing missing 12 M 2 32 2 10000.00 10000.00 13 M 1 35 3 missing missing 14 F 2 23 4 100000.00 50000.00 15 F 2 34 1 64000.00 64000.00 16 M 1 26 2 Missing missing 17 M 1 36 3 missing missing 18 F 0 41 4 7500.00 5500.00 19 F 0 43 1 missing missing…rofessor Cornish studied rainfall cycles and sunspot cycles. (Reference: Australian Journal of Physics, Vol. 7, pp. 334-346.) Part of the data include amount of rain (in mm) for 6-day intervals. The following data give rain amounts for consecutive 6-day intervals at Adelaide, South Australia. 7 28 7 1 69 3 1 4 22 7 16 4 54 160 60 73 27 3 3 1 7 144 107 4 91 44 1 8 4 22 4 59 116 52 4 155 42 24 11 43 3 24 19 74 26 63 110 39 34 71 52 39 8 0 15 2 14 9 1 2 4 9 6 10 (i) Find the median. (Use 1 decimal place.)(ii) Convert this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B a value below the median. Test the sequence for randomness about the median at the 5% level of significance. (b) Find the number of runs R, n1, and n2. Let n1 = number of values above the median and n2 = number of values below the median. R n1 n2 (c) In the case, n1 > 20, we cannot use Table 10 of Appendix II to find the critical…Consider the following information on ultimate tensile strength (lb/in) for a sample of n = 4 hard zirconium copper wire specimens (from “Characterization Methods for Fine Copper Wire,” Wire J. Intl., Aug., 1997: 74-80): X (bar)= 76,831 s = 180 smallest xi = 76,683 largest xi = 77,048Determine the values of the two middle sample observations (and don’t do it by successive guessing!).
- An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola. Beverage Sample Size Sample Mean Sample SD Strawberry Drink 10 535 24 Cola 10 559 15 Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value. (Use ? = 0.05.) State the relevant hypotheses. (Use ?1 for the strawberry drink and ?2 for the cola.) H0: ?1 − ?2 = 0Ha: ?1 − ?2 ≥ 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 ≠ 0 H0: ?1 − ?2 = 0Ha: ?1 − ?2 < 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 > 0 Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. Reject H0. The data suggests that cola has a higher average compression strength than the strawberry drink.Reject H0. The…The following data are from a random sample of 10 students who participated in a study undertaken to investigate the effect of sleep time (measured in average number of hours of sleep per night) on GPA (grade point average, measured on a 4-point scale). Student Sleep time GPA 1 7 3.28 2 9 3.16 3 8 3.75 4 6 2.50 5 4 2.45 6 8 2.91 7 7 3.53 8 6 3.02 9 3 2.30 10 8 3.48 a. Find the equation between GPA (y) as function of sleep time (x). b. What is the estimated GPA of a student who averages 5 hours of sleep per night? c. What is the coefficient of determination? *(no use EXCEL)Following is the data related to the daily production of the two factories of same product located in two different states. Factory Daily Production Factory 1 66 66 73 83 74 73 73 69 82 71 73 66 67 80 79 78 Factory 2 66 63 71 65 65 67 57 48 71 73 68 58 62 81 60 62 72 72 57 77 68 Calculate the critical values “ttab”, and tcal
- A random sample of companies in electric utilities (I), financial services (II), and food processing (III) gave the following information regarding annual profits per employee (units in thousands of dollars). I II III 49.9 55.4 39.2 43.9 25.0 37.5 32.7 41.9 10.1 27.8 29.6 32.6 38.1 39.6 15.7 36.5 42.3 20.5 Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.) SSTOT = SSBET = SSW = Find d.f.BET, d.f.W, MSBET, and MSW. (Use 3 decimal places for MSBET, and MSW.) dfBET = dfW = MSBET = MSW = Find the value of the sample F statistic. (Use 3 decimal places.) What are the degrees of freedom? Find the P-value of the sample test statistic. Make a summary table for your ANOVA test.Kaitlyn measures the upload speed in megabits per second of her home broadband internet connection during peak hours and off-peak hours. The results are provided in the accompanying table. Peak Off-Peak 5.83 5.14 6.05 6.80 7.14 6.98 3.54 5.77 5.45 7.27 5.90 6.62 5.81 6.19 4.82 6.08 6.37 6.59 4.65 5.58 5.30 7.41 6.48 6.26 5.96 6.37 5.79 6.31 6.84 6.55 5.06 4.95 5.61 7.03 6.45 6.77 Examine the results of Kaitlyn's test to determine the statements that compare the medians and interquartile ranges of the data sets to each other in terms of this situation. Select the two correct answers. The median upload speed during peak hours is 5.905 megabits per second, which is less than the median upload speed during off-peak hours, 7.005 megabits per second. The upload speeds during peak hours are slower on average compared to off-peak times. The median upload speed during peak hours is 6.37 megabits per second, which is greater than the median upload speed during…Refer to Exercise 8.S.6. Analyze these data using a Wilcoxon signed-rank test.
- In each of Exercises, use the Wilcoxon signed-rank test to perform the required hypothesis test. Global Warming? During the late 1800s, Lake Wingra in Madison, Wisconsin, was frozen over an average of 124.9 days per year. A random sample of eight recent years provided the following data on numbers of days that the lake was frozen over. 103 80 79 135 134 77 80 111 At the 5% significance level, do the data provide sufficient evidence to conclude that the average number of ice days is less now than in the late 1800s?The following data represent the number of audience members per week at a theater in Paris during the last year. (The theater was closed for 2 weeks for refurbishment.)163 165 094 137 123 095 170 096 117 129152 138 147 119 166 125 148 180 152 149167 120 129 159 150 119 113 147 169 151116 150 110 110 143 090 134 145 156 165174 133 128 100 086 148 139 150 145 100Estimate the average weekly attendance with a 95% interval estimate.Six samples of each of four types of cereal grain grown in a certain region were analyzed to determine thiamin content, resulting in the following data (µg/g). Wheat 5.3 4.4 6.1 6.1 6.6 5.8 Barley 6.4 8.1 6.2 7.5 5.9 5.6 Maize 5.7 4.8 6.5 5.0 6.1 5.2 Oats 8.2 6.1 7.9 7.1 5.4 7.3 Does this data suggest that at least two of the grains differ with respect to true average thiamin content? Use a level ? = 0.05 test.State the appropriate hypotheses. H0: ?1 ≠ ?2 ≠ ?3 ≠ ?4 Ha: at least two ?i's are equal H0: ?1 = ?2 = ?3 = ?4 Ha: at least two ?i's are unequal H0: ?1 = ?2 = ?3 = ?4 Ha: all four ?i's are unequal H0: ?1 ≠ ?2 ≠ ?3 ≠ ?4 Ha: all four ?i's are equal Compute the test statistic value. (Round your answer to two decimal places.)f = What can be said about the P-value for the test? P-value > 0.100 0.050 < P-value < 0.100 0.010 < P-value < 0.050 0.001 < P-value < 0.010 P-value < 0.001 State the conclusion in the problem context. Reject H0.…