Observing that the proportion of blue candies in his bowl appeared to be less than that of the other colors, a student decided to compare the color distribution in randomly chosen bags of the candy to the theoretical distribution reported by the candy company's consumer affairs. For his study, the student bought three bags of the colored candies from local stores and counted the number of each color. The average number of each color in the three bags (rounded to the nearest integer) was distributed as shown to the right. Use this data to complete parts (a) through (c). Color Frequency Brown 152 Yellow 115 Red 106 Orange 51 Green 45 Blue 45 a. Obtain a relative-frequency distribution. Color Frequency Relative Frequency Brown 152 Yellow 115 Red 106 Orange 51 Green 45 Blue 45 (Round to three decimal places as needed.)
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Step 1: Calculate the total number of candies by adding up the frequency of each color: Total = 152 (Brown) + 115 (Yellow) + 106 (Red) + 51 (Orange) + 45 (Green) + 45 (Blue) Show more…
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A manufacturer of colored candies states that 13% of the candies in a bag should be brown, 14% yellow, 13% red, 24% blue, 20% orange, and 16% green. A student randomly selected a bag of colored candies. He counted the number of candies of each color and obtained the results shown in the table. Test whether the bag of colored candies follows the distribution stated above at the α = 0.05 level of significance. Determine the null and alternative hypotheses. Choose the correct answer below: A. H0: The distribution of colors is not the same as stated by the manufacturer. H1: The distribution of colors is the same as stated by the manufacturer. B. H0: The distribution of colors is the same as stated by the manufacturer. H1: The distribution of colors is not the same as stated by the manufacturer. C. None of these. Compute the expected counts for each color. (Round to two decimal places.) Observed Distribution of Colors Color Observed Count Brown 59 Yellow 67 Red 56 Blue 59 Orange 97 Green 63 Claimed proportions: Brown 0.13, Yellow 0.14, Red 0.13, Blue 0.24, Orange 0.20, Green 0.16.
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A manufacturer of colored candies states that 13% of the candies in a bag should be brown, 14% yellow, 13% red, 24% blue, 20% orange, and 16% green. A student randomly selected a bag of colored candies. He counted the number of candies of each color and obtained the results shown in the table. Test whether the bag of colored candies follows the distribution stated above at the α=0.05 level of significance. Compute the expected counts for each color. Color Frequency Expected Count Brown 5959 ? Yellow 6666 ? Red 5454 ? Blue 6161 ? Orange 9090 ? Green 6565 ? (Round to two decimal places as needed.)
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M\&M Colors. Observing that the proportion of I3.29 Mam Colors. blue M\&Ms in his bowl of candy appeared to be less than that of the other colors, R. Fricker, Jr., decided to compare the color distribution in randomly chosen bags of M\&Ms to the theoretical distribution reported by M\&M/MARS consumer affairs. Fricker published his findings in the article "The Mysterious Case of the Blue M\&Ms" (Chance, Vol. 9(4), pp. 19-22). The following is the theoretical distribution. $$\begin{array}{l|c} \hline \text { Color } & \text { Percentage } \\ \hline \text { Brown } & 30 \\ \text { Yellow } & 20 \\ \text { Red } & 20 \\ \text { Orange } & 10 \\ \text { Green } & 10 \\ \text { Blue } & 10 \\ \hline \end{array}$$ For his study, Fricker bought three bags of M\&Ms from local stores and counted the number of each color. The average number of each color in the three bags was distributed as follows.
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