Suppose that under H0, a measurement X is N(0, σ2) and that under H1, X is...
Suppose that under H0, a measurement X is N(0, σ2) and that
under H1, X is
N(1, σ2) and that the prior probability P(H0) = 2×P(H1).As in
Section 9.1, the
hypothesis H0 will be chosen if P(H0|x) > P(H1|x). For σ2 = 0.1,
0.5, 1.0, 5.0:
a. For what values of X will H0 be chosen?
b. In the long run, what proportion of the time will H0 be chosen
if H0 is true 2
3 of the time?
Homework Answers
Add Answer to:
Suppose that under H0, a measurement X is N(0, σ2) and that
under H1, X is...
Consider the test of H0 : σ2-5 against H1 : σ2 < 5. Approximate the P-value...
Consider the test of H0 : σ2-5 against H1 : σ2 < 5. Approximate the P-value for the following test statistic. 215.2 and n 12 0.01 < P-value < 0.05 0.25< P-value 0.75 0.5< P-value < 0.9 0.1 < p-value < 0.5 O 0.05<P-value< 0.09
n = 81 s2 = 625 H0: σ2 = 500 Ha: σ2 ≠ 500 9. The...
n = 81 s2 = 625 H0: σ2 = 500 Ha: σ2 ≠ 500 9. The test statistic equals a. 100 b. 101.88 c. 101.25 d. 64 10. The p-value is between a. 0.025 and 0.05 b. 0.05 and 0.1 c. 0.1 and 0.2 d. 0.2 and 0.3 11. What is your conclusion? Use α = 0.05. a. fail to reject the null hypothesis b. reject the null hypothesis
H0: P=0.6 versus H1 P>0.6 n=200, x=135, a=0.1 a) What is the P value? b) Do...
H0: P=0.6 versus H1 P>0.6 n=200, x=135, a=0.1 a) What is the P value? b) Do we reject or accept the null hypothesis?
Suppose you want to test the following hypotheses: H0: p ≥ 0.4 vs. H1: p <...
Suppose you want to test the following hypotheses: H0: p ≥ 0.4 vs. H1: p < 0.4. A random sample of 1000 observations was taken from the population. Answer the following questions and show your Excel calculation for each question clearly: (a) Let p ̂ be the sample proportion. What is the standard error of sample proportion (i.e., σ_p ̂ ) if H0 is true? (b) If the sample proportion obtained were 0.38 (i.e., p ̂=0.38), what is its p-value?...
Suppose that X1, X2, . . . , Xn is an iid sample of N (0, σ2 ) observations, where σ 2 > 0 is unknown. Consider testing H0 : σ 2 = σ 2 0 versus H1 : σ 2 6= σ 2 0
Suppose that X1, X2, . . . , Xn is an iid sample of N (0, σ2
) observations, where σ
2 > 0 is
unknown. Consider testing
H0 : σ
2 = σ
2
0 versus H1 : σ
2
6= σ
2
0
;
where σ
2
0
is known.
(a) Derive a size α likelihood ratio test of H0 versus H1. Your rejection region should
be written in terms of a sufficient statistic.
(b) When the null...
2. A randon sample XI, X. is drawn frotn Normal(μ, σ2), where-oo < μ < oo and 0 < σ2 < x. To test the null hypothesis Ho : σ2-1 against the alternative H1: σ2 > 1, we have designed the...
2. A randon sample XI, X. is drawn frotn Normal(μ, σ2), where-oo < μ < oo and 0 < σ2 < x. To test the null hypothesis Ho : σ2-1 against the alternative H1: σ2 > 1, we have designed the following test Reject Ho if S>k where S2 = "LE:-1(x,-X)2, k ís a constant. Noticed that (n-1) distribution with degree of freedom 1 has a (a) Determine k so that the test will have size a. (b) Use k...
Consider the hypothesis test H0:μ1=μ2 against H1:μ1<μ2 with known variances σ1=10 and σ2=5. Suppose that sample...
Consider the hypothesis test H0:μ1=μ2 against H1:μ1<μ2 with
known variances σ1=10 and σ2=5. Suppose that sample sizes n1=10 and
n2=15 and that x¯1=14.2 and x¯2=19.7. Use α=0.05.
Font Paragraph Styles Chapter 10 Section 1 Additional Problem 1 Consider the hypothesis test Ho : = 12 against HI : <H2 with known variances = 10 and 2 = 5. Suppose that sample sizes nj = 10 and 12 = 15 and that I = 14.2 and 72 = 19.7. Use a...
Consider testing the hypotheses: H0: p = 0.56 H1: p > 0.56 where p is the...
Consider testing the hypotheses: H0: p = 0.56 H1: p > 0.56 where p is the true current proportion of employed U.S. adults who feel that basic mathematical skills are critical or very important to their job. Suppose a larger sample is selected. Suppose we take a random sample of 160 employed adults and finds that 110 of them feel that basic mathematical skills are critical or very important to their job. a) Using the larger sample of size n...
Exercises 10.3. Let Xi . . . , x N μ, σ2), whereơ2 s known to be equal to 100. In testing Ho : 25...
Exercises 10.3. Let Xi . . . , x N μ, σ2), whereơ2 s known to be equal to 100. In testing Ho : 25vs. H :H>25,h What sample size n would be necessary if one wishes to reject Ho with probability at least 95 if μ 26? iid se that a coin is to be tossed n times, and you wish to test the hypothesis Ho:p-12 VS. Hi P> I/2 at a- .05. What sample size n would be...
1 For the hypothesis test H0 mu<=5 against H1: mu >5 with variance unknown and n=11,...
1 For the hypothesis test H0 mu<=5 against H1: mu >5 with variance unknown and n=11, find the best approximation for the P-value for the test statistic t0=1.945. 0.25 ≤ p ≤ 0.50 0.10 ≤ p ≤ 0.25 0.010 ≤ p ≤ 0.025 0.025 ≤ p ≤ 0.050 0.0025 ≤ p ≤ 0.0050 2 The probability of type II error increases if the difference between the hypothesized values of the parameter increases, assuming that the sample size and other parameters...
Consider the test of H0 : σ2-5 against H1 : σ2 < 5. Approximate the P-value for the following test statistic. 215.2 and n 12 0.01 < P-value < 0.05 0.25< P-value 0.75 0.5< P-value < 0.9 0.1 < p-value < 0.5 O 0.05<P-value< 0.09
2. A randon sample XI, X. is drawn frotn Normal(μ, σ2), where-oo < μ < oo and 0 < σ2 < x. To test the null hypothesis Ho : σ2-1 against the alternative H1: σ2 > 1, we have designed the following test Reject Ho if S>k where S2 = "LE:-1(x,-X)2, k ís a constant. Noticed that (n-1) distribution with degree of freedom 1 has a (a) Determine k so that the test will have size a. (b) Use k...
Consider the hypothesis test H0:μ1=μ2 against H1:μ1<μ2 with
known variances σ1=10 and σ2=5. Suppose that sample sizes n1=10 and
n2=15 and that x¯1=14.2 and x¯2=19.7. Use α=0.05.
Font Paragraph Styles Chapter 10 Section 1 Additional Problem 1 Consider the hypothesis test Ho : = 12 against HI : <H2 with known variances = 10 and 2 = 5. Suppose that sample sizes nj = 10 and 12 = 15 and that I = 14.2 and 72 = 19.7. Use a...
Exercises 10.3. Let Xi . . . , x N μ, σ2), whereơ2 s known to be equal to 100. In testing Ho : 25vs. H :H>25,h What sample size n would be necessary if one wishes to reject Ho with probability at least 95 if μ 26? iid se that a coin is to be tossed n times, and you wish to test the hypothesis Ho:p-12 VS. Hi P> I/2 at a- .05. What sample size n would be...
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 11 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 11 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 11 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 11 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 11 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 11 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 11 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 11 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 11 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 11 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 11 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 11 months ago