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 locall

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.

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Eliza 2 months 2021-10-17T15:11:09+00:00 1 Answer 0 views 0

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    2021-10-17T15:12:16+00:00

    Answer:

    As Z<-Z_{\alpha}, 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<-1.56

    As Z<-Z_{\alpha}, 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.

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