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Corn Production The data in the table represent the number of corn plants in randomly sampled rows (a 17-foot by 5-inch strip) for various types of plot. An agricultural researcher wants to know whether the mean number of plants for each plot type is equal.

(a) Write the null and alternative hypotheses.

(b) State the requirements that must be satisfied to use the oneway ANOVA procedure.

(c) Use the following partial Minitab output to test the hypothesis of equal means at the  level of significance.

(d) Shown are side-by-side boxplots of each type of plot. Do these boxplots support the results obtained in part (c)?

(e) Verify that the -test statistic is 7.10.

(f) Verify the residuals are normally distributed.

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Compatibility with the 3G network, Wi-Fi and a touch screen are other recent features of mobile phones. The previous table also contains data on 3G compatibility and whether the phone has Wi-Fi and touch screen (a ‘1’ indicates the phone has 3G compatibility, Wi-Fi, and touch screen, respectively and a ‘0’ that is does not). Develop another multiple regression model using the four explanatory variables (battery standby time, music player score, camera resolution, and weight) and the three dummy variables 3G, Wi-Fi, and touch screen. Summarize the strength of your model (including the dummy variables) and any new variables generated by recoding. What advice would you give to mobile phone manufacturers with regard to the development, release and marketing of new mobile phones?

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Heart Rate of Smokers A researcher wants to determine the effect that smoking has on resting heart rate. She randomly selects seven individuals from three categories: (1) nonsmokers, (2) light smokers (fewer than 10 cigarettes per day), and (3) heavy smokers (10 or more cigarettes per day) and obtains the following heart rate data (beats per minute):

(a) Test the null hypothesis that the mean resting heart rate for each category is the same at the  level of significance. Note: The requirements for a one-way ANOVA are satisfied.

(b) If the null hypothesis is rejected in part (a), use Tukey’s test to determine which pairwise means differ using a familywise error rate of .

(c) Draw boxplots of the three treatment levels to support the results obtained in parts (a) and (b).

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Reaction Time In an online psychology experiment sponsored by the University of Mississippi, researchers asked study participants to respond to various stimuli. Participants were randomly assigned to one of three groups: Group 1, the simple group, required to respond as quickly as possible after a stimulus was presented; Group 2, the go/no-go group, required to respond to a particular stimulus while disregarding other stimuli; and Group 3, the choice group, required to respond differently depending on the type of whistle sound, the subject must press a certain button. The researcher wants to determine if the mean reaction times for each stimulus are equal. The reaction time (in seconds) for each stimulus is presented in the table.

(a) What type of experimental design is this?

(b) What is the response variable? What is the explanatory variable? How many levels of treatment are there in this experiment?

(c) State the null and alternative hypotheses.

(d) Verify that the requirements to use the one-way ANOVA procedure are satisfied. Normal probability plots indicate that the sample data come from a normal population.

(e) Test the hypothesis that the mean reaction times for the three stimuli are the same at the  level of significance.

(f) Draw boxplots of the three stimuli to support the analytic results obtained in part (c).

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