To shorten the time it takes him to make his favorite pizza, a student designed an experiment to test the effect of sugar and milk on the activation times for baking yeast. Specifically, he tested four different recipes and measured how many seconds it took for the same amount of dough to rise to the top of a bowl. He randomized the order of the recipes and replicated each treatment 4 times. Here are the boxplots of activation times from the four recipes: State the hypotheses about the recipes (both numerically and in words). Based on the boxplots above, would you reject or fail to reject the null hypothesis? Explain your reasoning by using the ideas of MSG and MSE. Would it be appropriate to follow up this study with multiple comparisons to see which recipes differ in their mean activation times? Explain

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  1. To shorten the time it takes him to make his favorite pizza, a student designed an experiment to test the effect of sugar and milk on the activation times for baking yeast. Specifically, he tested four different recipes and measured how many seconds it took for the same amount of dough to rise to the top of a bowl. He randomized the order of the recipes and replicated each treatment 4 times.

    Here are the boxplots of activation times from the four recipes:
    1. State the hypotheses about the recipes (both numerically and in words).
    2. Based on the boxplots above, would you reject or fail to reject the null hypothesis? Explain your reasoning by using the ideas of MSG and MSE.
    3. Would it be appropriate to follow up this study with multiple comparisons to see which recipes differ in their mean activation times? Explain.

This image shows a box plot comparing the activation times (in seconds) for four different recipes, labeled A, B, C, and D. The Y-axis represents activation times in seconds, ranging from 0 to 800.

- **Recipe A**: The box plot reveals a range of activation times between approximately 400 and 600 seconds. The median is around 500 seconds.
  
- **Recipe B**: Activation times range from around 200 to 300 seconds, with a median close to 250 seconds.

- **Recipe C**: Shows a range from about 600 to 700 seconds, with the median near 650 seconds.

- **Recipe D**: Displays a range from approximately 250 to 350 seconds, with a median around 300 seconds.

Each box represents the interquartile range (IQR) where the middle 50% of observations fall, with the lines (whiskers) indicating variability outside the quartiles. The lines inside the boxes represent the median values for each recipe.
Transcribed Image Text:This image shows a box plot comparing the activation times (in seconds) for four different recipes, labeled A, B, C, and D. The Y-axis represents activation times in seconds, ranging from 0 to 800. - **Recipe A**: The box plot reveals a range of activation times between approximately 400 and 600 seconds. The median is around 500 seconds. - **Recipe B**: Activation times range from around 200 to 300 seconds, with a median close to 250 seconds. - **Recipe C**: Shows a range from about 600 to 700 seconds, with the median near 650 seconds. - **Recipe D**: Displays a range from approximately 250 to 350 seconds, with a median around 300 seconds. Each box represents the interquartile range (IQR) where the middle 50% of observations fall, with the lines (whiskers) indicating variability outside the quartiles. The lines inside the boxes represent the median values for each recipe.
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