Question

For each of the following situations, identify the type of interval or test you would

perform. Include hypothesis test or confidence interval, mean or proportion, one sample or two sample

(independent or dependent for two samples). An example of an answer

would be “hypothesis test, proportion, two samples, independent, and prop.test(fill in the correct pieces)”

Do not do the test or find the confidence interval.

8. (6 pts) Random samples of professional football and basketball players gave the following weights in

pounds.

Football: 245 262 255 251 244 276 240 265 257 252 282

Basketball: 205 200 220 210 191 215 221 216 228 207 225 208

Use a significance level of 5% to test the claim that the mean weight of professional football players is

greater than the mean weight of professional basketball players.

Answer 1

The test is hypothesis test, difference in means, two samples, independent, and t.test

Use R function t.test () to perform the T-test:

x <- c(245, 262, 255 ,251, 244, 276, 240 ,265, 257 ,252 ,282)
y <- c(205, 200 ,220 ,210, 191, 215, 221, 216 ,228, 207 ,225, 208)
t.test(x, y , mu = 0,alternative = "greater", var.equal = FALSE)

OUTPUT:

   Welch Two Sample t-test

data: x and y
t = 8.9175, df = 19.364, p-value = 1.374e-08
alternative hypothesis: true difference in means is greater than 0
95 percent confidence interval:
36.29493 Inf
sample estimates:
mean of x mean of y
257.1818 212.1667

Since the P-value = 0.000000014 < , we reject the null hypothesis.

Conclude that mean weight of professional football players is greater than the mean weight of professional basketball players.