To evaluate the effectiveness of a new type of plant food developed for tomatoes, an experiment was conducted in which a random sample of 33 seedlings was obtained from a large greenhouse having thousands of seedlings. Each of the 33 plants received 42.5 grams of this new type of plant food each week for 28 weeks. The number of tomatoes produced by each plant was recorded yielding the following results:

X=33.15 s=4.392

 

(a) Assuming that the seedlings chosen are taken from a population which is normally distributed, determine a 95%

95% confidence interval estimate for the average number of tomatoes that would have been produced by all the seedlings in the greenhouse if they have recieved 42.5 grams of thee new plant food, once a week for 28 weeks. Use three decimals. 

 

lower bound:

upper bound:

 

(b) The greenhouse is currently using a plant food called "Supr-Grow". The average number of tomatoes produced by seedlings in the greenhouse with "Supr-Grow" is 32. Based on the interval in (a), should the greenhouse switch to the new plant food? (YES or NO)

 

(c) A researcher has started with a new sample and a given degree of confidence that the average number of tomatoes the seedlings produced on the new plant food is between "34.68318 and 37.95682". Suppose the sample size and standard deviation are the same as given above. What alpha did the researcher use in the construction of this statement?

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