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- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1In a population if you have µ = 10, σ = 2, and your z-score is +1.5, what is the value of X?t the Blood Bank, they know that O+ blood is the most common blood type and that 40%40% of the people are known to have O+ blood. Blood type A- is a very scarce blood type and only 6%6% of the people have A- blood. Half of the people have blood type A or B. Let: X=X= number of people who have blood type O+ Y=Y= number of people who have blood type A- Z=Z= number of people who have blood type A or B
- Let X have a mean of 13 and a variance of 1.1. Let Y have a mean of 9.1 and a variance of 0.75. The covariance of x and y is 0.35. Let Z=4X – 5Y+2. What is the mean and variance of Z?Find the z-score corresponding to a score of X = 45 μ = 40 and σ = 20 μ = 40 and σ =10 μ = 40 and σ = 5 μ = 40 and σ = 2Explain Which of the following would have the largest influence? (h is the leverage, R is the studentized residual)X:1, Y:2, h:0.39, R:1.2X:2, Y:3, h:1.23, R:-0.13X:3, Y:5, h:1.21, R:-1.68
- A researcher wants to determine if the exam scores of the students are dependent on the length of time spent in studying the subject. Ten students in a certain class were taken and the results are shown in the table below where X is the time spent in studying the subject in hours and Y is the examination scores. X (time) Y (score) 1.5 80 3.0 83 1.25 83 0.5 70 3.5 85 2.5 75 1.0 70 3.0 90 2.5 86 4.0 91 If a test for the significance of r is conducted at 0.05 level of significance, what is the value of the t statistic? (rounded to 1 decimal placeFor the following data (0, 22), (15, 24), (18, 37), (22, 25), (24, 123) what three data points of x should you choose for quadratic interpolation to find y(14.9)?An analyst in the real estate business is interested in the relationship between the cost of the monthly rent of an apartment and the size of an apartment, in big cities. She gathers data for apartment buildings in 12 cities in 12 different states. In each city, she gets the numbers for at least 5 different buildings and at least 40 apartments in each building. She reaches the following conclusion: the rental cost of a 2-bedroom apartment is 50% more than the rental cost of a 1-bedroom apartment, and the rental cost of a 3-bedroom apartment is 50% more than the rental cost of a 2-bedroom apartment. Based on the paragraph, what is the minimum number of apartments she collected data on? Do you think her sample was large enough to be statistically valid? Based on the paragraph, are there any apartments or apartment buildings that she would have excluded from her study? Do you see any bias in how she selected apartments for her study? Based on the paragraph, is there a positive…
- The director of a local Tourism Authority would like to know whether a family’s annual expenditure on recreation (y), measured in $000s, is related to their annual income (x), also measured in $000s. In order to explore this potential relationship, the variables x and y were recorded for 10 randomly selected families that visited the area last year. The results were as follows: Week 1 2 3 4 5 6 7 8 9 10 x 41.2 50.1 52.0 62.0 44.5 37.7 73.5 37.5 56.7 65.2 y 2.4 2.7 2.8 8.0 3.1 2.1 12.1 2.0 3.9 8.9 The summary statistics for these data are: Sum of x data: 520.4 Sum of the squares of x data: 28431.42 Sum of y data: 48 Sum of the squares of y data: 343.74 Sum of the products of x and y data: 2858.63 (i) Draw a scatter diagram of these data.The director of a local Tourism Authority would like to know whether a family’s annual expenditure on recreation (y), measured in $000s, is related to their annual income (x), also measured in $000s. In order to explore this potential relationship, the variables x and y were recorded for 10 randomly selected families that visited the area last year. The results were as follows: Week 1 2 3 4 5 6 7 8 9 10 x 41.2 50.1 52.0 62.0 44.5 37.7 73.5 37.5 56.7 65.2 y 2.4 2.7 2.8 8.0 3.1 2.1 12.1 2.0 3.9 8.9 The summary statistics for these data are: Sum of x data: 520.4 Sum of the squares of x data: 28431.42 Sum of y data: 48 Sum of the squares of y data: 343.74 Sum of the products of x and y data: 2858.63 Calculate the sample correlation coefficient. Interpret the findings.