Question

A seed company is researching the consistency in the output of a new hybrid tomato plant that was recently developed. The weights of the random sample of 91 tomatoes produced by the hybrid plant are measured in pounds and the sample has a variance of 0.0225. Construct a 95% confidence interval for the variance in weights for all tomatoes produced by the new hybrid plant. Assume the hybrid tomato weights are normally distrusted.

a. verify that the conditions hold.

b. State the required standard score(s) (z, t, or χ2):

c. Set up the confidence interval fully, without simplifying (graded on paper).

(d) Then simplify and state your final answer:

Answer 1

Given that

sample size = n=91

sample variance =

Confidence level=C=0.95

A) The assumptions of confidence interval are

1) The data must be sampled randomly

2) The sample values are must be independent to each other

3) Identically the data must be drawn from normally distribyted population

Here all the assumtions are satiesfied

B) By using test we can calculate required confidence interval

Here we want to calculate 95% confidence interval for the variance in weights for all tomatoes produced by the new hybrid plant

Where

.........( By using chi square table)

.......( By using chi square table)C

C) The 95% confidence interval for the variance in weights for all tomatoes produced by the new hybrid plant is

i.e.

i.e. ...................( Answer)

D) Interpretation: if we repeted take samples and calculate 95% confidence interval for the variance for each sample for weights for all tomatoes produced by the new hybrid plant then approximate 95 times the population variance should lie between (0.0171, 0.0308).........( Answer)