STA 412 HW 04 (ANOVA) Question: 1 Total Points: 30 30 Bonus Points: Score: 0 0 1. A large laboratory has four types of devices used to determine the pH of soil samples. The laboratory wants to determine whether there are differences in the average readings given by these devices. A bag of soil is collected and randomly divided into 24 soil samples. So all the soil samples have the same pH. Soil samples are randomly assigned to each device and then tested. The response recorded is the the pH reading of the device. These values, along with summary statistics, are given in the following table. pH readings Sample Sample Sample Device 1 2 3 4 5 6 Size Mean Standard deviation A 6.35 6.41 6.78 6.72 6.56 6.38 6 6.533 0.184 B 6.52 6.57 6.57 6.78 6.79 7.06 6 6.715 0.204 C 6.94 6.64 7.04 6.65 7.02 6.85 6 6.857 0.177 D 6.65 7.19 6.6 6.87 6.92 6.88 6 6.852 0.212 (a) (5 points) The goal is to investigate whether there are differences in pH readings for the four devices. Write down the null and alternative hypotheses. (b) (5 points) Input the data into R, and calculate sample size, mean and variance for each samples with function aggregate and also calculate the overall mean and sample size. (c) (10 points) Assume that the assumptions for one-way ANOVA are satisfied. Starting with the summary statistics of each sample, fill in the numbers in the following ANOVA table. Show your calculation details. df SS MS F-statistic Between-sample Within-sample (d) (5 points) Type the sample data into R and use R to create an ANOVA table. Attach the R output. What is the p-value of the F test? Is the null hypothesis rejected? (e) (5 points) What are the assumptions needed for the one-way ANOVA in b and c?