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Question: Is your random number generator working? Use your calculator's RandInt function to generate 200 digits from 0 to 9 and store them in a list.
(a) State appropriate hypotheses for a chi-square test for goodness of fit to determine whether your calculator's random number generator gives each digit an equal chance to be generated.
(b) Carry out a test at the a = 0.05 significance level.
(c) What is the probability that a student who does this exercise will make a Type I error?
(d) Suppose that 25 students in an AP Statistics class independently do this exercise for homework. Find the probability that at least one of them makes a Type I error.
The time to failure of a nickel-cadmium battery is Weibull-distributed with parameters v=0 α = 1/2 years and β = 1/4. Find the fraction of batteries that are expected to fail prior to 1.5 years.
Let R be a σ-ring of subsets of a set X . Let S be the σ-algebra generated by R. Recall (§3.3, Problem 8) or prove that S consists of all sets in R and all complements of sets in R.
Suppose X¯ t = 5.1 with sw = 7 based on n = 25. Test the hypothesis that the population trimmed mean is exactly 4.8 with α = 0.01.
the diameter of small nerf balls manufactured at a factory in china is expected to be approximately normally
In terms of parameter a, random variable X has CDF
In the context of this scenario, what would be the consequences of making a Type I error?
Girls' cross-country times: a contrast (optional). Continue your analysis of the data from the previous problem by comparing average race time during the first half of the season with the average for the second half.
In the radar system of Example 8.4, the probability that a target is present is P[H1] = 0.01. In the case of a false alarm, the system issues an unnecessary alert at the cost of C10 = 1 unit.
What percentage of the college freshmen would be considered physically ?t if we consider only this part of the test?
According to an article in Travel and Leisure, every person in a small study of sleep during vacation was found to sleep longer than average during the first.
A common practice now is for large retail pharmacies to buy the customer base from smaller, independent pharmacies. The way this works is that the buyer.
suppose instead the data from problem 1 and 4 were taken on the same process thus the data are no longer independent.
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