The use of the interval P(1 -p) p + (z critical value), n requires a large sample. For each of the following combi- nations of n and p, indicate whether the given interval would be appropriate. a. n = 50 and p = .30 b. n = 50 and p = .05 c. n = 15 and p = .45 %3D d. n = 100 and p = .01 %3D
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- Find the critical value, z0, from the z table for the given parameters. a=0.20 two tailed testFind the critical value, z0, from the z table for the given parameters. a=0.10 left tailed testThe use of the interval p̂ ± (z critical value) p̂(1 − p̂) n requires a large sample. For each of the following combinations of n and p̂, indicate whether the sample size is large enough for use of this interval to be appropriate. a. n = 51 and p̂ = 0.30 Yes or No b. n = 51 and p̂ = 0.05 Yes or No c. n = 11 and p̂ = 0.45 Yes or No
- Let X1,...,Xn be iid exponential(θ) random variables. Derive the LRT of H0 : θ = θ0 versus Ha : θ 6= θ0. Determine an approximate critical value for a size-α test using the large sample approximation.From exercise 9-15 Find the boundary of the critical region if the type I error probability is a) alpha = 0.01 and n = 10 b) alpha = 0.05 and n=10 c) alpha = 0.01 and n=16 d) alpha = 0.05 and n=16 From exercise 9-15 standard deviation = 20 H0: mu = 175 H1: mu >175If you let X1, X2, X3, X4 equal the cholesterol level of a woman under the age of 50, a man under 50, a woman 50 or older, and a man 50 or older, respectively. Assuming the distribution of Xi is N(μi, σ2), i = 1, 2, 3, 4 and you test the null hypothesis H0: μ1 = μ2 = μ3 = μ4, using seven observations of each Xi, what would be the critical region for an alpha = 0.05 significance level?
- If X1 and X2 constitute a random sample of size n = 2from an exponential population, find the efficiency of 2Y1relative to X, where Y1 is the first order statistic and 2Y1and X are both unbiased estimators of the parameterFor a Student’s t-distribution with mean 0, standard deviation 1, and degrees of freedom 49, which of the following Python lines outputs the critical value a if ? Note: a is a constant. Select one. A import scipy.stats as stprint(st.t.ppf(0.135, 49, 0, 1)) B import scipy.stats as stprint(st.t.pdf(0.135, 49, 0, 1)) C import scipy.stats as stprint(st.t.sf(0.135, 49, 0, 1)) D import scipy.stats as stprint(st.t.cdf(0.135, 49, 0, 1))a. Determine the positive critical value Z* corresponding to:i. 87.64% confidence.ii.95.34% confidence.iii. 57.04% confidence.b. Which of these three z* values is largest? Which is smallest?The largest Z* value is the one associated with_____ %.The smallest Z* value is the one associated with____ %.
- . In general, a ____ t-statistic and a _____ p-value (relative to a chosen critical value and alpha) indicate that our estimated statistic is ____ to occur by chance if the null is true. a. Large; large; likely b. Small; large; likely c. Small; small; unlikely d. Large; large; likelyA random sample of 50 students was asked to estimate how much money they spent on textbooks in a year. The sample skewness of these amounts was found to be 0.83 and the sample kurtosis was 3.98. Test at the 10% level the null hypothesis that the population dis- tribution of amounts spent is normal..A sample of 9 measurements, randomly selected from a normally distributed population, resulted in x= 2.6, and s= 0.9 Conduct a hypothesis test to verify the claim that the population mean is greater than 2.5 . Use a=.05