Susan is interested in determining whether sunflower seedlings treated with comp

Question

Susan is interested in determining whether sunflower seedlings treated with compound A resulted in a lower average height of sunflower seedlings than the standard height of 15.7 cm. She treated a random sample of 10 seedlings with compound A and then recorded their heights: 11.5, 15.2, 16.5, 15.1, 12.9, 9.3, 11.8, 15, 8.5 and 9.5. Assuming sunflower seedlings are normally distributed and that Susan must estimate the standard deviation of this distribution, which of the following statements properly analyzes Susan’s hypothesis:

Select one:

a. She needs to conduct a two-tailed t-test; although the average of the sample is below 15.7 she cannot reject the null hypothesis at the 5% level.

b. She needs to conduct a one-sided t-test; the average of the sample is below 15.7 and statistically significant at the 5% level.

c. She needs to conduct a two-tailed z-test; although the average of the sample is below 15.7 she cannot reject the null hypothesis at the 5% level.

d. She needs to conduct a one-sided z-test; the average of the sample is below 15.7 and statistically significant at the 5% level.

e. She needs to conduct a two-tailed t-test; the average of the sample is below 15.7 and statistically significant at the 5% level.

Explanation / Answer

Since Susan need to compare the sample mean with a hypothesized value and standard deviation of the population is not known,

She needs to conduct a one-sided t-test; the average of the sample is below 15.7 and statistically significant at the 5% level.

Option B is correct.

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