Question

construct all random samples consisting 2 observation from the given data you are asked to guess the average weight of 6th watermelons by taking a random sample without replacement from the population

Answer 1

Watermelon A B C D E F

Weight (in pounds) 19 14 15 9 10 17

Random samples consisting 2 observation:

$(19,14),(19,15),(19,10),(19,9),(19,17),(14,15),(14,9),(14,10),$

$(14.17),(15,9),(15,10),(15,17),(9,10),(9,17),(10,17)$

For sample size n=5:

$(19, 14, 15, 9, 10),\overline{x}=13.4$

$(19, 14, 15, 9, 17),\overline{x}=14.8$

$(19, 14, 15, 10, 17),\overline{x}=15$

$(19, 14, 9, 10, 17),\overline{x}=13.8$

$(19, 15, 9, 10, 17),\overline{x}=14$

$(14, 15, 9, 10, 17),\overline{x}=13$

 The average weight of 6th watermelons by taking a random sample without replacement:

$\mu=\frac{13.4+14.8+15+13.8+14+13}{6}=14\ pounds$