Refer to Exercise 12.5. Consider two methods for selecting the dosages. Method 1 assigns three rats to the dosage x = 2 and three rats to x = 5. Method 2 equally spaces the dosages between x = 2 and x = 5 (x = 2, 2.6, 3.2, 3.8, 4.4, and 5.0). Suppose that σ is known and that the relationship between E(Y) and x is truly linear (see Chapter 11). If we use the data from both methods to construct confidence intervals for the slope β1, which method will yield the longer interval? How much longer is the longer interval? If we use method 2, approximately how many observations will be required to obtain an interval the same length as that obtained by the optimal assignment of method 1?
12.5 Suppose that we wish to study the effect of the stimulant digitalis on the blood pressure Y of rats over a dosage
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Mathematical Statistics with Applications
- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardRespiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.arrow_forwardRepeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forward
- bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.arrow_forwardThe following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.arrow_forward
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