6. Data on the number of calories per serving for randomly selected cereals from three different brands (General Mills, Kellogg's, and Kashi) are summarized in the provided plot and table. 250 200 Brand General Mills 26 125.77 41.10 150 Kashi 16 178.13 39.02 Kellogg's Overall 33 141.52 43.24 100 75 143.87 45.38 50 General Mils Kashi Kelogg's Brand (a) State the appropriate null and alternative hypotheses for testing if the mean calories per serving differs among the three brands. (You could write it in symbols or words) (b) What are the conditions for using ANOVA? Does it seems reasonable to assume these conditions are satisfied for this data? Explain briefly. (c) Complete the following partial ANOVA table and use it to answer questions below. Df Sum Sq Mean Sq F value Pr(>F) cerealbrands 27476 13738 0.00078 Error 72 124903 Total 152379 (d) State the conclusion of the test in context (Use a = 0.05) Calories Per Serving

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.