(t Test (in Excel) for Two Samples with Unequal Variances) In an agricultural experiment, the effects of two fertilizers on the production of oranges were measured. Fourteen randomly selected plots of land were treated with fertilizer A, and 10 randomly selected plots were treated with fertilizer B. The number of pounds of harvested fruit was measured from each plot. Following are the results. Fertilizer A Fertilizer B 448, 478,482, 442,455, 480 ,457, 506, 436,478,453,489,400,444,495,438,481,501 470,444, 466, 427, 461, 431 Assume that the populations are approximately normal. Can you conclude that there is a difference in the mean yields for the two types of fertilizer? Use the α = 0.01 level of significance. Use Excel to perform the hypothesis test. State the null and alternate hypotheses that would be appropriate for this hypothesis test. Use proper notation and formatting. Give the value of the test statistic. Round to three decimal places if needed. Give the p-value of the test statistic. Round to four decimal places if needed. Using the p-value method, should be rejected at the level of significance? Why or why not? Choose an appropriate conclusion based on your decision in part d. There is a difference in the mean yields of oranges for the two types of fertilizer. There is not enough evidence to conclude that there is a difference in the mean yields for the two types of fertilizer.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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(t Test (in Excel) for Two Samples with Unequal Variances) In an agricultural experiment, the effects of two fertilizers on the production of oranges were measured. Fourteen randomly selected plots of land were treated with fertilizer A, and 10 randomly selected plots were treated with fertilizer B. The number of pounds of harvested fruit was measured from each plot. Following are the results.

Fertilizer A Fertilizer B

448, 478,482, 442,455, 480 ,457, 506, 436,478,453,489,400,444,495,438,481,501

470,444, 466, 427, 461, 431

Assume that the populations are approximately normal. Can you conclude that there is a difference in the mean yields for the two types of fertilizer? Use the α = 0.01 level of significance.

Use Excel to perform the hypothesis test.

State the null and alternate hypotheses that would be appropriate for this hypothesis test. Use proper notation and formatting.

Give the value of the test statistic. Round to three decimal places if needed.

Give the p-value of the test statistic. Round to four decimal places if needed.

Using the p-value method, should be rejected at the level of significance? Why or why not?

Choose an appropriate conclusion based on your decision in part d.

There is a difference in the mean yields of oranges for the two types of fertilizer.

There is not enough evidence to conclude that there is a difference in the mean yields for the two types of fertilizer.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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