Question

A brochure claims that the average maximum height for a certain type of plant is 0.7 m. A gardener suspects that this is not accurate locally due to variation in soil conditions, and believes the local height is shorter. A random sample of 40 mature plants is taken. The mean height of the sample is 0.65 m with a standard deviation of 0.20 m. Test the claim that the local mean height is less than 0.7 m using a 5% level of significance.

Answer 1

Answer:

As $Z$, it is possible to reject null hypotesis. It means that the local mean height is less tha 0.7 m with a 5% level of significance.

Step-by-step explanation:

1. Relevant data:

$\mu=0.70\\N=40\\\alpha=0.05\\X=0.65\\s=0.20$

2. Hypotesis testing

$H_{0}=\mu=0.70$

$H_{1} =\mu< 0.70$

3. Find the rejection area

From the one tail standard normal chart, whe have Z-value for $\alpha=0.05$ is 1.56

Then rejection area is left 1.56 in normal curve.

4. Find the test statistic:

$Z=\frac{X-\mu_{0} }{\sigma/\sqrt{n}}$

$Z=\frac{0.65-0.70}{0.20/\sqrt{40}}\\Z=-1.58$

5. Hypotesis Testing

$Z_{\alpha}=1.56\\Z=-1.58$

$-1.58$

As $Z$, it is possible to reject null hypotesis. It means that the local mean height is less tha 0.7 m with a 5% level of significance.