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 random sample of n = 72 plants received a certain amount of this new type of plant food each week for 14 weeks. The variable of interest is the number of tomatoes produced by each plant in the sample. The table below reports the descriptive statistics for this study: Variable Descriptive statistics for the tomato food study sample sample mean standard deviation 72 56.00 8.00 standard error number of tomatoes 0.943 Assuming the population is normally distributed, the investigators would like to construct a 90% confidence interval for the average number of tomatoes that all plants of this variety can produce when fed this supplement like this. a) The margin of error is: (3 decimals) b) The corresponding 90% confidence interval for the true population mean is: Lower Limit: (3 decimals) to Upper Limit: (3 decimals) c) What would we conclude at a = 0.1 for the hypothesis test Ho: u = 59.671 vs. H We do not have enough evidence to conclude the true mean is 59.671. y # 59.671? We do not have enough evidence to conclude the true mean is 56.00. We have enough evidence to conclude that the true mean is 59.671. We have sufficient evidence to conclude that the true mean is different from 59.671. We have insufficient evidence to conclude the true mean is different from 59.671.

Answer 1

The margin of error is computed below: ME = t. SE(F) As the population standard deviation is unknown, so a t-test statistic will be used to compute the margin of error. Degrees of freedom = n-1 = 72 - 1 = 71 The critical value of t-test statistic is computed using MS-Excel function as 1.666. The screenshot of the MS-Excel function is attached below: fr =T.INV.27(0.1,71) The margin of error is computed below: ME =1.666 x 0.943 = 1.5710 Thus, the margin of error is 1.571 b) The 90% confidence interval for the population mean is computed below:

CI = F ME(F) = 56 +1.571 =(56-1.571, 56+1.571) = (54.429,57.571) Lower limit = 54.429| Upper limit = 57.571 The hypothesis to be tested is: Ho: d = 59.671 H: 4 59.671 The hypothesized mean does not lie in the 90% confidence interval, so the null hypothesis will be rejected at 10% level of significance. We do not have enough evidence to conclude that the true mean is 59.671.