A soft drink manufacturer wants to determine the proportion of its soda cans that meet quality standards. A quality control engineer randomly selects 2000 cans off the assembly line and finds that 99.7% (1994 of the 2000) meet quality standards. Step 2 of 4: What is the parameter of interest?
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Parameter:
Any statistical measure based on all the units in the population is called a Parameter.
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- 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…Roy ‘s Texaco wants to keep the price of its unleaded gasoline competitive with that of other stations in the area. Roy’s is currently charging $1.29 per gallon. To check that the average price for this gasoline for all stations within a 15 mile radius is higher than his price, Roy randomly samples the price of unleaded gasoline at ten stations located in this area. He obtains the following data for the price per gallon (in dollars): 1.7, 1.5, 2.6, 2.2, 2.4, 2.3, 2.6, 3.0, 1.4, 2.3 Set up the appropriate hypotheses and test them using a significance level of α= .05Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: x 1 2 3 4 5 y 15.8 18.1 14.4 19.6 20.0 Σx = 15; Σy = 87.9; Σx2 = 55; Σy2 = 1,568.77; Σxy = 273.6 (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.) x = y = b = ŷ = + x
- The toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. Here are data for beak heat loss, as a percent of total body heat loss from all sources, at various temperatures in degrees Celsius. [Note: The numerical values in this problem have been modified for testing purposes.] Temperature (oC)(oC) 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Percent heat loss from beak 33 33 34 31 37 46 54 49 41 50 44 56 55 61 64 59 The equation of the least-squares regression line for predicting beak heat loss, as a percent of total body heat loss from all sources, from temperature is: (Use decimal notation. Enter the values of the intercept and slope rounded to two decimal…Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: x 1 2 3 4 5 y 14.2 17.7 14.4 19.6 20.0 Σx = 15; Σy = 85.9; Σx2 = 55; Σy2 = 1,506.45; Σxy = 271.2 (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.) x = y = b = ŷ = + x (b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram. (c) Find the sample correlation coefficient r and the coefficient of determination r2. (Round your answers to three decimal places.) r = r2 = What percentage of variation in y is explained…A group of students need to submit a project and they need to survey people about their daily routine. How many people should they survey in order to be 95% confident that the estimated ( sample) proportion is within three percentage points of the true population? Assume that pq= 0.25
- 2. In the mid-19th century, Sir Francis Galton demonstrated, through extensive data collection, that many human characteristics such as height and IQ are distributed throughout the entire population in accordance with the normal distribution. Galton recorded the heights of 8585 men in Great Britain. This forms a normal distribution with mean u = 67 inches and standard deviation o = 2.5inches.Perform PCA or principle component analysis on the following data: х1 x2 x3 810.6 13.4 42.93 1775 24.2 32.319 430.4 5.7 60.434 459.8 9 21.398 802.4 13.9 55.778 279.6 20.4 53.236 288.4 4.6 63.208 152.7 7.3 59.727 253.4 9.9 48.037 358.6 13.5 48.288 72 12.8 36.507 205 5.9 37.195 253.6 15.8 36.964 416.5 12.3 42.83 1075.9 17.1 39.684 Answer the following questions based on the PCA: • How many principle components were created? • What percent of total variance is accounted for by the calculated principal components? (Round to 2 decimal places) • What are the weights for computing the first principle component scores? (Round to 4 decimal places) o x1: • x2: o x3:Joan's Nursery specializes in custom-designed landscaping for residential areas. The estimated labor cost associated with a particular landscaping proposal is based on the number of plantings of trees, shrubs, and so on to be used for the project. For cost-estimating purposes, managers use two hours of labor time for the plant- ing of a medium-sized tree. Actual times from a sample of 10 plantings during the past month follow (times in hours).2.1 2.2 1.7 1.6 2.3 3.1 1.5 2.6 2.4 2.2 With a .05 level of significance, test to see whether the mean tree-planting time differs from two hours. a. State the null and alternative hypotheses. b. Compute the sample mean. c. Compute the sample standard deviation. d. What is the p-value? e. What is your conclusion?
- The Fish and Game Department stocked a lake with fish in the following proportions: 30% catfish, 15% bass, 40% bluegill, and 15% pike. Five years later it sampled the lake to see if the distribution of fish had changed. It found that the 500 fish in the sample were distributed as follows. Catfish Bass Bluegill Pike 122 75 222 81 In the 5-year interval, did the distribution of fish change at the 0.05 level Find the value of the chi-square statistic for the sample. Estimate the P-value of the sample test statistic. P-value > 0.100 0.050 < P-value < 0.100 0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.005 < P-value < 0.010 P-value < 0.005 Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories? Since the P-value > α, we fail to reject the null hypothesis. Since the P-value > α, we reject the null hypothesis. Since the…Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: x 1 2 3 4 5 y 12.2 20.9 14.4 19.6 20.0 Σx = 15; Σy = 87.1 ; Σx2 = 55; Σy2 =1577.17; Σxy = 275.6 (a) Draw a scatter diagram. (b) Find the equation of the least-squares line. (Round your answers to two decimal places.) ŷ = + x (c) Find r. Find the coefficient of determination r2. (Round your answers to three decimal places.) r = r2 = Explain what these measures mean in the context of the problem. The correlation coefficient r measures the strength of the linear relationship between a bighorn sheep's age and the mortality rate. The coefficient of determination r2 measures the explained…The population proportion for a certain characteristic is 0.28. In a sample of 100 people, 25 had that characteristic. Which equation correctly describes the point estimate? OA. p=0.25 О В. р%3D0.25 O C. p= 0.28 D. p 0.28