DATA:
```
Trt A Trt B Trt C Trt D Trt E
1 42.0 57.5 42.1 47.6 47.3
2 38.7 39.3 58.9 37.1 53.9
3 57.8 53.7 28.9 58.8 39.0
4 22.8 59.1 25.7 56.9 28.5
```
Evaluate:
```
H_0: μ_A = μ_B = μ_C = μ_D = μ_E
against
H_A: μ_A ≠ μ_B ≠ μ_C ≠ μ_D ≠ μ_E
```

1. What is the calculated F statistic? (round to the nearest thousandth; place your answer in the box below)

2. Evaluate the F calculated for the treatment effect, and indicate if you are going to reject (R) or fail to reject (FR) the null hypothesis using α=0.100 (R/FR; place your answer right beside the calculated F statistic)

Full credit will be given if 1 and 2 are correct.

To round the calculated F statistics to the nearest thousandth and indicate whether you are going to reject (R) or fail to reject (FR) the null hypothesis using an α = 0.100.

1. To calculate the F statistics, we need to perform a one-way analysis of variance (ANOVA) on the given data. The formula for calculating the F statistics is:

F = (SSbetween / (k - 1)) / (SSwithin / (n - k))

where SSbetween is the sum of squares between treatments, SSwithin is the sum of squares within treatments, k is the number of treatments, and n is the total number of observations.

To calculate SSbetween, we need to find the sum of squares for each treatment. We can do this by calculating the sum of squares for each treatment and then summing them up:

SSbetween = (n1 * (mean1 - grand_mean)^2) + (n2 * (mean2 - grand_mean)^2) + ... + (nk * (meank - grand_mean)^2)

where n1, n2, ..., nk are the number of observations in each treatment, mean1, mean2, ..., meank are the means of each treatment, and grand_mean is the mean of all the observations.

To calculate SSwithin, we need to find the sum of squares within each treatment. We can do this by calculating the sum of squares for each treatment and then summing them up:

SSwithin = (sum of squares for treatment A) + (sum of squares for treatment B) + ... + (sum of squares for treatment E)

Once we have calculated SSbetween and SSwithin, we can substitute them into the formula to calculate the F statistics.

2. To evaluate the F calculated for the treatment effect and determine whether to reject or fail to reject the null hypothesis, we need to compare the calculated F value with the critical F value at the desired significance level (α).

In this case, the null hypothesis (H0) states that the means of all treatments are equal, while the alternative hypothesis (HA) states that at least one mean is different. We will reject the null hypothesis if the calculated F value is greater than the critical F value, and fail to reject the null hypothesis if the calculated F value is less than or equal to the critical F value.

To find the critical F value, we need to look it up in the F-distribution table using the degrees of freedom for the numerator (k - 1) and the degrees of freedom for the denominator (n - k).

Once we have the critical F value, we can compare it with the calculated F value to determine whether to reject or fail to reject the null hypothesis.

Learn more about F-distribution from this link :

https://brainly.com/question/22780219

#SPJ11