# Question: Among the data collected for the World Health Organization air

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 centers (commercial districts), of Melbourne and Houston, respectively. Using n = 13 observations of X and m = 16 observations of Y, we shall test H0: μX = μY against H1: μX < μY.

(a) Define the test statistic and critical region, assuming that the variances are equal. Let α = 0.05.

(b) If = 72.9, sx = 25.6, = 81.7, and sy = 28.3, calculate the value of the test statistic and state your conclusion.

(c) Give bounds for the p-value of this test.

(a) Define the test statistic and critical region, assuming that the variances are equal. Let α = 0.05.

(b) If = 72.9, sx = 25.6, = 81.7, and sy = 28.3, calculate the value of the test statistic and state your conclusion.

(c) Give bounds for the p-value of this test.

**View Solution:**## Answer to relevant Questions

Let X and Y equal the forces required to pull stud No. 3 and stud No. 4 out of a window that has been manufactured for an automobile. Assume that the distributions of X and Y are N(μX, σ2x) and N(μY, σ2Y), ...Let p be the fraction of engineers who do not understand certain basic statistical concepts. Unfortunately, in the past, this number has been high, about p = 0.73. A new program to improve the knowledge of statistical ...In Exercise 8.2-13, data are given that show the effect of a certain fertilizer on plant growth. The growths of the plants in mm over six weeks are repeated here, where Group A received fertilizer and Group B did not: We ...Let X1, X2, X3 be a random sample of size n = 3 from an exponential distribution with mean θ > 0. Reject the simple null hypothesis H0: θ = 2, and accept the composite alternative hypothesis H1: θ < 2, if the observed sum ...Referring back to Exercise 6.4-19, find the likelihood ratio test of H0: γ = 1, μ unspecified, against all alternatives.Post your question