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Let Liz-1 eforthe conditional distribution f PrivenX)--Pr(z-2 I. Solve for the conditional distribution of Z given X-x....
Figure 1. Vertical li indicate the 2.5% tails of the alternate distribution. In other words, the ...
please answer questions
Figure 1. Vertical li indicate the 2.5% tails of the alternate distribution. In other words, the red areas (area 0 and 8) sum to 5%, and areas 2, 3, 7 also sums to 5%. dicate the 2.5% tails of the null distribution, while B and D alternate distribution null distribution test statistic Consider a two-sided null hypothesis test with 0.05 as significance level. From the above probability density plot, identify the corresponding areas, or test statistic value...
part iii and iv Exercise 3 (Paired test, known variance of the difference). Let X, Y...
part iii and iv
Exercise 3 (Paired test, known variance of the difference). Let X, Y be RVs. Denote E[X] = Hx and E[Y] = My. Suppose we want to test the null hypothesis Houx = uy against the alternative hy- pothesis H :Mx My. Suppose we have i.i.d. pairs (X1,Y),...,(Xn, Yn) from the joint distribution of (X,Y). Further assume that we know the value of o2 = Var(X-Y). (i) Noting that X1 - Y1,...,xn - Yn are i.i.d. with...
1. The joint pdf of (X,Y) is given by f(x,y) = Ce^(-ax - by), 0 0...
1. The joint pdf of (X,Y) is given by f(x,y) = Ce^(-ax - by), 0 0 and b> 0 i) Determine the value of C. ii) Determine correlation between X and Y. iii) Determine the conditional distribution of X, given Y=y. iv) Let Z=XY. Compute E(Z) and Var(Z).
Question 1 Consider the simple regression model (only one covariate): y= BoB1 u Let B1 be the OLS estimator of B1. a) W...
Question 1 Consider the simple regression model (only one covariate): y= BoB1 u Let B1 be the OLS estimator of B1. a) What are the six assumptions needed for B1 to be unbiased, have a simple expression for its variance, and have normal distribution? (3 points) b) Under Assumptions 1-6, derive the distribution of B1 conditional on x\,..., xn. (3 points) In lecture we described how to test the null hypothesis B1 bo against the alternative hypothesis B1 bo, where...
Exercise 4 (Paired test, known normality of the difference). Let X, Y be RVs. Denote E[X]...
Exercise 4 (Paired test, known normality of the difference). Let X, Y be RVs. Denote E[X] = 4x and E[Y] = uy. Suppose we want to test the null hypothesis Houx = My against the alternative hy- pothesis H ux #uy. Suppose we have i.i.d. pairs (X1,Y),...,(X,Y) from the joint distribution of (X,Y). Further assume that we know the X - Y follows a normal distribution. (i) Noting that X1 - Y1,..., Xn-Ynare i.i.d. with normal distribution, show that (exactly)...
Say you think that an output will be normally distributed with mean 1 and variance 1 You use the test statistic r- 1 a) At what values of x would you reject the null if your a value is set to 0.05. H...
Say you think that an output will be normally distributed with mean 1 and variance 1 You use the test statistic r- 1 a) At what values of x would you reject the null if your a value is set to 0.05. Hint: there are two values xŻ and xk such that if x x; or if x x, we would reject. b) Say that in actuality, z is drawn from an exponential distribution with mean 1. Thus the null...
Question 2. Suppose (X.,X) . FXY, for i = 1, , n. We collect sample data for n-100, obtain sz-2 and Sy-1, and would like to test H0 : Var(x)-Var(y) versus HA : Var(z) Var(y). (a) Using the F test, wh...
Question 2. Suppose (X.,X) . FXY, for i = 1, , n. We collect sample data for n-100, obtain sz-2 and Sy-1, and would like to test H0 : Var(x)-Var(y) versus HA : Var(z) Var(y). (a) Using the F test, what is the observed statistic? (b) Derive the null distribution and write out the p-value.
Question 2. Suppose (X.,X) . FXY, for i = 1, , n. We collect sample data for n-100, obtain sz-2 and Sy-1, and would like...
The marital status distribution of the U.S. male population, age 15 and older, is as shown...
The marital status distribution of the U.S. male population, age 15 and older, is as shown below. Marital Status Percent never married 31.3 married 56.1 widowed 2.5 divorced/separated 10.1 Suppose that a random sample of 400 U.S. young adult males, 18 to 24 years old, yielded the following frequency distribution. We are interested in whether this age group of males fits the distribution of the U.S. adult population at the 5% level. Calculate the frequency one would expect when surveying...
I. Matching Write your answers in the blanks provided. (2 pt. each) 8. The symbol used...
I. Matching Write your answers in the blanks provided. (2 pt. each) 8. The symbol used in the alternate hypothesis to indicate it is a two-tailed test. ___________ 9. Every null hypothesis is written with what type of equality or inequality symbol? __________ 10. In hypothesis testing, the level of significance α describes the probability of making a ____________ error. __________ 11. In hypothesis testing, if the P-value < α , _____________ the null hypothesis. __________ 12. In hypothesis testing,...
PART F PART i In 1955, Life Magazine reported that a 25-year-old mother of three worked,...
PART F PART i
In 1955, Life Magazine reported that a 25-year-old mother of three worked, on average, an 80 hour week. Recently, many groups have been studying whether or not the women's movement has, in fact, resulted in an increase in the average work week for women (combining employment and at-home work). Suppose a study was done to determine if the mean work week has increased. 68 women were surveyed with the following results. The sample mean was 83;...
please answer questions
Figure 1. Vertical li indicate the 2.5% tails of the alternate distribution. In other words, the red areas (area 0 and 8) sum to 5%, and areas 2, 3, 7 also sums to 5%. dicate the 2.5% tails of the null distribution, while B and D alternate distribution null distribution test statistic Consider a two-sided null hypothesis test with 0.05 as significance level. From the above probability density plot, identify the corresponding areas, or test statistic value...
part iii and iv
Exercise 3 (Paired test, known variance of the difference). Let X, Y be RVs. Denote E[X] = Hx and E[Y] = My. Suppose we want to test the null hypothesis Houx = uy against the alternative hy- pothesis H :Mx My. Suppose we have i.i.d. pairs (X1,Y),...,(Xn, Yn) from the joint distribution of (X,Y). Further assume that we know the value of o2 = Var(X-Y). (i) Noting that X1 - Y1,...,xn - Yn are i.i.d. with...
Question 1 Consider the simple regression model (only one covariate): y= BoB1 u Let B1 be the OLS estimator of B1. a) What are the six assumptions needed for B1 to be unbiased, have a simple expression for its variance, and have normal distribution? (3 points) b) Under Assumptions 1-6, derive the distribution of B1 conditional on x\,..., xn. (3 points) In lecture we described how to test the null hypothesis B1 bo against the alternative hypothesis B1 bo, where...
Exercise 4 (Paired test, known normality of the difference). Let X, Y be RVs. Denote E[X] = 4x and E[Y] = uy. Suppose we want to test the null hypothesis Houx = My against the alternative hy- pothesis H ux #uy. Suppose we have i.i.d. pairs (X1,Y),...,(X,Y) from the joint distribution of (X,Y). Further assume that we know the X - Y follows a normal distribution. (i) Noting that X1 - Y1,..., Xn-Ynare i.i.d. with normal distribution, show that (exactly)...
Say you think that an output will be normally distributed with mean 1 and variance 1 You use the test statistic r- 1 a) At what values of x would you reject the null if your a value is set to 0.05. Hint: there are two values xŻ and xk such that if x x; or if x x, we would reject. b) Say that in actuality, z is drawn from an exponential distribution with mean 1. Thus the null...
Question 2. Suppose (X.,X) . FXY, for i = 1, , n. We collect sample data for n-100, obtain sz-2 and Sy-1, and would like to test H0 : Var(x)-Var(y) versus HA : Var(z) Var(y). (a) Using the F test, what is the observed statistic? (b) Derive the null distribution and write out the p-value.
Question 2. Suppose (X.,X) . FXY, for i = 1, , n. We collect sample data for n-100, obtain sz-2 and Sy-1, and would like...
PART F PART i
In 1955, Life Magazine reported that a 25-year-old mother of three worked, on average, an 80 hour week. Recently, many groups have been studying whether or not the women's movement has, in fact, resulted in an increase in the average work week for women (combining employment and at-home work). Suppose a study was done to determine if the mean work week has increased. 68 women were surveyed with the following results. The sample mean was 83;...
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