Question

A sample of 80 plants were paired together by genetic similarities. In each pair one plant was given Fertilizer A and the other Fertilizer B. After a month using these fertilizers the increases in height were recorded the passenger seat. The 40 differences in heights (A-B) had a mean of -0.8 cm.with a standard deviation 3.3 cm. We wish to know if Fertilizer B makes plants grow faster.

Answer 1

We cannot conclude that Fertilizer B has a positive effect on plant growth.

How to determine growth?

To determine whether Fertilizer B makes plants grow faster, perform a hypothesis test.

Null Hypothesis (H₀): Fertilizer B has no effect on plant growth, meaning the average difference in height (A-B) is equal to 0 cm.

Alternative Hypothesis (H₁): Fertilizer B makes plants grow faster, meaning the average difference in height (A-B) is less than 0 cm.

Significance Level (α): 0.05

Sample Mean (
`\overline x`): -0.8 cm

Sample Standard Deviation (s): 3.3 cm

Test Statistic (z): (
`\overline x` - μ₀) / (s / √n)

= (-0.8 - 0) / (3.3 / √80)

= -1.52

Now, compare the test statistic (z) to the critical values for the significance level (α) of 0.05.

For a one-tailed test (since we are only interested in one direction, the average difference being less than 0), find the critical value that corresponds to the area in the tail of the standard normal distribution that is equal to α = 0.05.

This critical value is approximately -1.645.

Since the test statistic (-1.52) is greater than the critical value (-1.645), we fail to reject the null hypothesis.

Conclusion:

The sample data does not provide sufficient evidence to conclude that Fertilizer B makes plants grow faster. The average difference in height (A-B) is not significantly different from 0 cm. Therefore, we cannot conclude that Fertilizer B has a positive effect on plant growth.