5. (11 pts) A farmer would like to evaluate Miracle Grow when used on his potted

Question

5. (11 pts) A farmer would like to evaluate Miracle Grow when used on his potted daisy plants. He sets up 20 plants in a room all facing the same window aining the same amount of sunlight, and waters them identically each day. For a month, he monitors how much each plant grows. Then, he adds Miracle Grow to every pot and monitors how much each plant grows during a month with Miracle Grow. At the end of two months, he discovers that 16 plants grew more with Miracle Grow. Test the hypothesis that Miracle Grow increases plant growth (using an alpha level of.01). a. (2 pts) What is the appropriate test? b. (1 pt) State the null hypothesis: c. (1 pt) State the alternative hypothesis: d. (2 pts) Find the critical value: e. (1 pt) Calculate the obtained statistic: f. (2 pts) Make a decision: g. (2 pts) What does your decision mean? a ditribution and why is it important for inferentialnh tio

Explanation / Answer

Question 5

(a) Here the most appropriate test is non paramatric sign test.

(b) Null hypothesis : H0 : p = 0.5 where p is proportion of plants grow by Miracle grow is equal to proportion of plant grow naturally.

(c) ALternative Hypothesis : Ha : p > 0 where p is the proportion of plants grow by Miracle grow is more than the proportion of plant grow naturally.

(d) Here the critical value is c if so BIN (x >= c ; 20 ; 0.5) < 0.01

so here c = 15

decision rule is reject the null hypothesis if N+ >= 15

(e) Here test statistic T = 16

(f) Here T > critical value c so we reject the null hypothesis

(g) Here our decision means that miracle grow helps plants grow in size better than in normal conditions.

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