Question

You think that your tree planting buddies are not sharpening their shovels often enough (or perhaps well enough). For 8 of your friends, you measure the number of trees they plant on Tuesday morning, Then you (who are a master shovel sharpener) sharpen each of their shovels during the evening so that they will have a razor sharp shovel the next morning. Then you measure the number of trees each of them plant on Wednesday morning. Do you have enough evidence (at α=.05) to conclude that your expert sharpening increased their production?

Planter Tuesday Wednesday

Akeera 600 600

Batoul 1100 1200

Chloe 900   800

Dylan 800 1000

Ethan   1000 1100

Francisco 700 800

George 300 400

Hope 400 400

Answer 1

let us consider the null and alternative hypothesis '

Ho:μ (tuesday) - μ (wednesday)= 0

Ha:μ (tuesday) - μ (wednesday)<0(one tailed )

Two-Sample T-Test and CI: tuesday, wednesday

Two-sample T for tuesday vs wednesday

N Mean StDev SE Mean
tuesday 8 725 282 100
wednesday 8 788 304 108

Difference = μ (tuesday) - μ (wednesday)
Estimate for difference: -63
95% upper bound for difference: 196
T-Test of difference = 0 (vs <): T-Value = -0.43 P-Value = 0.338 DF = 14
Both use Pooled StDev = 293.2271

since the p value of t statistic is 0.338 which is greter than 0.05 so we reject Ho and conclude that  your expert sharpening increased their production