# Question

Let X and Y denote the weights in grams of male and female common gallinules, respectively. Assume that X is N(μX, σ2x) and Y is N(μY, σ2Y).

(a) Given n = 16 observations of X and m = 13 observations of Y, define a test statistic and a critical region for testing the null hypothesis H0: μX = μY against the one-sided alternative hypothesis H1: μX > μY. Let α = 0.01. (Assume that the variances are equal.)

(b) Given that = 415.16, s2x = 1356.75, = 347.40, and s2y = 692.21, calculate the value of the test statistic and state your conclusion.

(c) Although we assumed that σ2x = σ2Y, let us say we suspect that that equality is not valid. Thus, use the test proposed by Welch

(a) Given n = 16 observations of X and m = 13 observations of Y, define a test statistic and a critical region for testing the null hypothesis H0: μX = μY against the one-sided alternative hypothesis H1: μX > μY. Let α = 0.01. (Assume that the variances are equal.)

(b) Given that = 415.16, s2x = 1356.75, = 347.40, and s2y = 692.21, calculate the value of the test statistic and state your conclusion.

(c) Although we assumed that σ2x = σ2Y, let us say we suspect that that equality is not valid. Thus, use the test proposed by Welch

## Answer to relevant Questions

Among the data collected for the World Health Organization air quality monitoring project is a measure of suspended particles, in μg/m3. Let X and Y equal the concentration of suspended particles in μg/m3 in the city ...For developing countries in Africa and the Americas, let p1 and p2 be the respective proportions of babies with a low birth weight (below 2500 grams). We shall test H0: p1 = p2 against the alternative hypothesis H1: p1 > ...A charter bus line has 48-passenger and 38- passenger buses. Let m48 and m38 denote the median number of miles traveled per day by the respective buses. With α = 0.05, use the Wilcoxon statistic to test H0: m48 = m38 ...Let X1, X2, ... , X8 be a random sample of size n = 8 from a Poisson distribution with mean λ. Reject the simple null hypothesis H0: λ = 0.5, and accept H1: λ > 0.5, if the observed sum 8i=1 xi ≥ 8. (a) Compute the ...Consider a random sample X1, X2, . . . , Xn from a distribution with pdf f(x; θ) = θ(1 − x)θ−1, 0 < x < 1, where 0 < θ. Find the form of the uniformly most powerful test of H0: θ = 1 against H1: θ > 1.Post your question

0