In order to evaluate the effectiveness of a new type of plantfood that was developed for tomatoes, a study was conducted inwhich a random sample of n = 68 plants received a certainamount of this new type of plant food each week for 14 weeks. Thevariable of interest is the number of tomatoes produced by eachplant in the sample. The table below reports the descriptivestatistics for this study:
Descriptive statistics for the tomato food study| Variable | n | sample mean | sample standard deviation | standard error |
| number of tomatoes | 68 | 60.00 | 9.60 | 1.164 |
Assuming the population is normally distributed, the investigatorswould like to construct a 98% confidence interval for the averagenumber of tomatoes that all plants of this variety can produce whenfed this supplement like this.
a) The margin of error is:Â Â (3 decimals)
b) The corresponding 98% confidence interval for the truepopulation mean is:
Lower Limit:Â Â (3 decimals)
to
Upper Limit:Â Â (3 decimals)
c) What would we conclude at α = 0.02 for the hypothesistest H0: μ = 64.875 vs. Ha:μ ≠64.875?
We do not have enough evidence to conclude the true mean is64.875.We have insufficient evidence to conclude the true mean isdifferent from 64.875.    We do not have enoughevidence to conclude the true mean is 60.00.We have enough evidenceto conclude that the true mean is 64.875.We have sufficientevidence to conclude that the true mean is different from64.875.
