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A company that specializes in products for home gardening has developed a new plant food that...

A company that specializes in products for home gardening has developed a new plant food that has been designed to increase the growing height of plants. The new plant food that has been tested on a sample of 12 plants of a type known to have a mean growing height of 18 inches. Results showed a sample mean height of 19.4 inches and a sample standard deviation of 3 inches. Assume that the heights of the plants are normally distributed. Using a .10 level of significance, is there reason to believe that the new plant food increases plant height?

Math   Statistics-And-Probability   
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Answer #1

H0: = 18

Ha: > 18

Test statistics

t = - / S / sqrt(n)

= 19.4 - 18 / 3 / sqrt(12)

= 1.62

This is test statistics value.

Critical value at 0.10 level with 11 df = 1.363

Since test statistics value > 1.363, we have sufficient evidence to reject H0.

We conclude at 0.10 level that we have sufficient evidence to support the claim.

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