(1 point) To evaluate the effectiveness of a new type of plant food developed fo
ID: 3333048 • Letter: #
Question
(1 point) To evaluate the effectiveness of a new type of plant food developed for tomatoes, an experiment was conducted in which a random sample of 57 seedlings was obtained from a large greenhouse having thousands of seedlings. Each of the 57 plants received 70 grams of this new type of plant food each week for 27 weeks. The number of tomatoes produced by each plant was recorded yielding the following results: X=38.17 s=4.13 (a) Assuming that the seedlings chosen are taken from a population which is normally distributed, determine a 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 70 grams of thee new plant food, once a week for 27 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 "33.23508 and 35.06492". 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? ti(Input your answer as a decimal)Explanation / Answer
here std error of mean =std deviation/(n)1/2 =4.13/(57)1/2 =0.5470
for (n-1=56) degree of freedom ;critical t =2.003
hence lower bound =sample mean -t*std error =37.07416
upper bound =sample mean +t*std error =39.26584
b) as our interval contain values above 32 ; hence yes
c)
for t critical =(35.06492-33.23508)/(2*0.5470)=1.672517
for above at 56 degree of freedom ; p value =alpha =0.10
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.