代写Introduction to Quantitative Methods ASSIGNMENT 1代做Python程序
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10 points
Q1 (3 points)
The propagation of fatigue cracks in various aircraft parts has been the subject of extensive study in recent years. The accompanying data consists of propagation lives (flight hours/104 ) to reach a given crack size in fastener holes intended for use in military aircraft (“Statistical Crack Propagation in Fastener Holes under Spectrum Loading,” J. Aircraft, 1983: 1028–1032):
0.736 0.863 0.865 0.913 0.915 0.937 0.983 1.007
1.011 1.064 1.109 1.132 1.140 1.153 1.253 1.394
a. Compute and compare the values of the sample mean and median.
b. By how much could the largest sample observation be decreased without affecting the value of the median?
Q2 (3 points)
A geologist has collected 10 specimens of basaltic rock and 10 specimens of granite. The geologist instructs a laboratory assistant to randomly select 15 of the specimens for analysis.
a. What is the pmf of the number of granite specimens selected for analysis?
b. What is the probability that all specimens of one of the two types of rock are selected for analysis?
c. What is the probability that the number of granite specimens selected for analysis is within 1 standard deviation of its mean value?
Q3 (4 points)
Two different companies have applied to provide cable television service in a region. Let p denote the proportion of all potential subscribers who favor the first company over the second. Consider testing H0: p = .5 versus Ha : p ≠ .5 based on a random sample of 25 individuals. Let X denote the number in the sample who favor the first company and x represent the observed value of X
a. Which of the following rejection regions is most appropriate and why?
R1 = {x: x ≤ 7 or x ≥ 18};
R2 = {x : x ≤ 8}; R3 = {x : x ≥ 17}
b. In the context of this problem situation, describe what type I and type II errors are.
c. What is the probability distribution of the test statistic X when H0 is true? Use it to compute the probability of a type I error.
d. Compute the probability of a type II error for the selected region when p = .3, again when p = .4, and also for both p = .6 and p = .7.
e. Using the selected region, what would you conclude if 6 of the 25 queried favored company 1?