Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.
-A brochure claims that the average maximum height of a certain type of plant is 0.7 meters. A gardener suspects that this estimate is not accurate locally due to soil conditions. A random sample of 48 mature plants is taken.
The mean height of the plants in the sample is 0.65 meters. Test whether the claim that the average maximum height is different from 0.7 meters is supported or not supported. Assume that the standard deviation is
0.2 meters.
A)supported
B)not supported

Question

Quizplus · Accepted Answer

Given the sample mean ($\bar{x}$) = 0.65 meters, the population mean ($\mu$) = 0.7 meters, the standard deviation ($\sigma$) = 0.2 meters, and the sample size (n) = 48. We are testing at a 0.05 significance level ($\alpha$) if the true mean height is different from 0.7 meters, which implies a two-tailed test.First, calculate the standard error (SE) of the mean:$$SE = \frac{\sigma}{\sqrt{n}} = \frac{0.2}{\sqrt{48}} = 0.02887$$Next, calculate the z-score:$$z = \frac{\bar{x} - \mu}{SE} = \frac{0.65 - 0.7}{0.02887} = -1.73$$For a two-tailed test at $\alpha = 0.05$, the critical z-values are approximately $\pm1.96$. Since our calculated z-value (-1.73) does not exceed the critical values, we fail to reject the null hypothesis. This means there is not enough evidence to support the claim that the average maximum height is different from 0.7 meters due to local soil conditions.

Conduct a Full Hypothesis Test and Determine If the Given