Homework 22

Problems

Instructions:

1. Use R to compute all sample statistics, \(P\)-values, and confidence intervals.
   • The x and y values are given below, so you do not have to type them in by hand. Use copy-and-paste.
2. Report a confidence interval or confidence bound (appropriate to the hypotheses under consideration) for the population correlation coefficient \(\rho_{X, Y}\) for the first three problems, and comment on (a) how precisely the population correlation coefficient has been estimated and (b) what the confidence interval indicates about the direction (positive or negative) and strength (weak or strong) of the linear association.
3. For problems that ask for a scatter plot, generate the scatter plot using R, print out the scatter plot, and attach the scatter plot to your homework.
4. For problems that ask you to perform a hypothesis test, you should follow the full 7-step procedure of stating the claim, determining the null and alternative hypotheses, etc.

Section 12.5:

1. 57
   • x = c(4200, 3600, 3750, 3675, 4050, 2770, 4870, 4500, 3450, 2700, 3750, 3300)
   • y = c(370, 340, 375, 310, 350, 200, 400, 375, 285, 225, 345, 285)
   • For Part d, generate a scatter plot using R, print the scatter plot, and attach to your homework. You do not need to construct normal probability plots.
   • For Part e, use a significance level of 0.01.
2. 58a,b,c,e
   • x = c(46, 48, 55, 57, 60, 72, 81, 85, 94, 109, 121, 132, 137, 148, 149, 184, 185, 187)
   • y = c(2.18, 2.10, 2.13, 2.28, 2.34, 2.53, 2.28, 2.62, 2.63, 2.50, 2.66, 2.79, 2.80, 3.01, 2.98, 3.34, 3.49, 3.26)
3. 59a
   • x = c(400, 750, 770, 800, 850, 1025, 1200, 1250, 1300, 1400, 1475, 1480, 1505, 2200)
   • y = c(3.80, 4.00, 4.90, 5.20, 4.00, 3.50, 6.30, 6.88, 7.55, 4.95, 7.80, 4.45, 6.60, 8.90)
   • Test the hypothesis at the 0.001 significance level.
4. 63ab