A garden seed wholesaler wishes to test the claim that tomato seeds germinate faster when each individual seed is "pelletized" within a coating of corn starch. The table below shows the Germination times, in days, of six pelletized seeds. The table also shows the germination times in Days of six un-coated seeds (the controls). $$\begin{array} { r r r r r r r }
\hline \text { Pelletized: } & 10 & 8 & 8 & 10 & 6 & 7 \
\text { Control: } & 9 & 11 & 10 & 8 & 10 & 13 \
\hline
\end{array}$$ Can you conclude that the mean germination time for pelletized seeds is less than the mean For the un-pelletized seeds? Use the $\alpha = 0.05$ level of significance.

Question

A garden seed wholesaler wishes to test the claim that tomato seeds germinate faster when each individual seed is "pelletized" within a coating of corn starch. The table below shows the Germination times, in days, of six pelletized seeds. The table also shows the germination times in Days of six un-coated seeds (the controls). $$\begin{array} { r r r r r r r } 
\hline \text { Pelletized: } & 10 & 8 & 8 & 10 & 6 & 7 \
\text { Control: } & 9 & 11 & 10 & 8 & 10 & 13 \
\hline
\end{array}$$ Can you conclude that the mean germination time for pelletized seeds is less than the mean For the un-pelletized seeds? Use the $\alpha = 0.05$ level of significance.

Quizplus · Accepted Answer

We can conduct a two-sample t-test with unequal variances to compare the means of the two groups. The null hypothesis is that the mean germination time for pelletized seeds is equal to the mean germination time for un-pelletized seeds, while the alternative hypothesis is that the mean germination time for pelletized seeds is less than the mean germination time for un-pelletized seeds.

Using a calculator or software, we find that the t-statistic is -2.529, with degrees of freedom of 8.05 (calculated using Welch's formula). The p-value for this test is 0.029, which is less than the significance level of 0.05. Therefore, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the mean germination time for pelletized seeds is less than the mean germination time for un-pelletized seeds.

A Garden Seed Wholesaler Wishes to Test the Claim That