In order to evaluate the effectiveness of a new type of plant food that was deve

ID: 3129894 • Letter: I

Question

In order to evaluate the effectiveness of a new type of plant food that was developed for tomatoes, a study was conducted in which a SRS of n = 13 plants - all of the same variety - received 10 grams of this new type of food each week for 14 weeks. The variable of interest is the number of tomatoes produced by each plant in the sample. Table 1 reports the descriptive statistics for this study:

The investigators would like to construct a 99% confidence interval for the true number of tomatoes that plants of this variety can produce when fed this supplement.
Note: you should carry at least 5 decimal precision for any intermediate calculations then round your answer as indicated in the problem

Table 1: Descriptive statistics for the tomato food study Variable n mean Std.Dev SEmean number of tomatoes 13 57.80 7.40 2.052

Explanation / Answer

A) The margin of error is:   6.27
     Round your answer to the nearest hundredth

B) The corresponding 99% confidence interval for the true population mean is: Low: 51  to High: 65 tomatoes

When setting confidence intervals for discrete data investigators will round the lower endpoint down to the next lowest integer and the upper endpoint up to the next highest integer. You should express your answers using this convention.

Confidence Interval Estimate for the Mean

Data

Sample Standard Deviation

7.4

Sample Mean

57.8

Sample Size

Confidence Level

99%

Intermediate Calculations

Standard Error of the Mean

2.052390726

Degrees of Freedom

t Value

3.0545

Interval Half Width

6.27

Confidence Interval

Interval Lower Limit

51.53

Interval Upper Limit

64.07