Question

In: Statistics and Probability

This dataset contains two variables: fertilizer type (1, 2, or 3) and crop yield per square...

This dataset contains two variables: fertilizer type (1, 2, or 3) and crop yield per square foot. Using ANOVA, test the null hypothesis that the three fertilizers are equally effective. Hint: Notice that the data are arranged in what's called a "long" format (one long column of data). To you ANOVA, you first need to rearrange the data into three columns.

1. What is the value of the F-statistic? Answer

2. What is the p-value that the three means are the same? Answer
3. At α=.05, should the null hypothesis be rejected? AnswerRejectDon’t reject

4. Which fertilizer should you choose based on these results (be careful here!)?

Data Set

fertilizer yield
1 177.228692
1 177.550041
1 176.408462
1 177.703625
1 177.125486
1 176.778342
1 176.746302
1 177.061164
1 176.274949
1 177.967203
1 176.6013
1 177.030543
1 177.479507
1 176.87413
1 176.114388
1 176.008395
1 176.108313
1 178.357441
1 177.262445
1 176.918845
1 176.239016
1 176.57307
1 176.039298
1 176.817922
1 176.160587
1 177.226424
1 175.938533
1 177.164937
1 175.36084
1 177.276996
1 175.945444
1 175.88278
2 176.479341
2 176.044342
2 177.412462
2 177.360818
2 177.385499
2 176.975808
2 177.379779
2 177.997995
2 176.434863
2 176.933265
2 175.98348
2 177.034093
2 176.436762
2 176.067745
2 177.121049
2 177.197721
2 176.603724
2 177.208171
2 177.148829
2 176.819077
2 176.999067
2 178.134605
2 176.429156
2 176.668323
3 177.104186
3 178.079635
3 176.903422
3 177.540284
3 177.03271
3 178.286042
3 176.40541
3 176.43083
3 177.396331
3 176.925576
3 177.055046
3 177.344164
3 177.128368
3 177.168302
3 176.353941
3 179.060899
3 176.300517
3 177.593352
3 177.115245
3 177.794457

Solutions

Expert Solution

Solution:

We can use the excel "ANOVA:Single Factor" data analysis tool to find the answer to the given questions. The excel output is given below:

Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
1 32 5656.22542 176.7570444 0.469119716
2 24 4246.255974 176.9273323 0.31409632
3 20 3545.018717 177.2509359 0.475272296
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 3.008554181 2 1.50427709 3.565667772 0.033304083 3.122102932
Within Groups 30.79710019 73 0.421878085
Total 33.80565437 75

1. What is the value of the F-statistic?

Answer: F = 3.566

2. What is the p-value that the three means are the same?

Answer: p-value = 0.0333
3. At α=.05, should the null hypothesis be rejected?

Answer: Reject

4. Which fertilizer should you choose based on these results (be careful here!)?

Answer: We should choose the fertilizer type 2

orchestra answered 2 years ago
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