A company claims they produce their mixed bag of candies so that, of the candies in the bag, 20 percent are dark chocolate, 60 percent are milk chocolate, and 20 percent are white chocolate. In a random sample of candies of size 50, the counts are as follows: 6 dark, 32 milk, and 12 white. Assuming the conditions for inference are met, what is the test statistic for a chi-square goodness-of-fit test to investigate whether the distribution of the sample is consistent with the company’s claim? A) χ2=62+322+122 B) χ2=102+302+102 C) χ2=(6−10)2+(32−30)2+(12−10)2 D) χ2=(6−10)210+(32−30)230+(12−10)210 E) χ2=(10−6)26+(30−32)232+(10−12)212
A company claims they produce their mixed bag of candies so that, of the candies in the bag, 20 percent are dark chocolate, 60 percent are milk chocolate, and 20 percent are white chocolate. In a random sample of candies of size 50, the counts are as follows: 6 dark, 32 milk, and 12 white. Assuming the conditions for inference are met, what is the test statistic for a chi-square goodness-of-fit test to investigate whether the distribution of the sample is consistent with the company’s claim?
A) χ2=62+322+122
B) χ2=102+302+102
C) χ2=(6−10)2+(32−30)2+(12−10)2
D) χ2=(6−10)210+(32−30)230+(12−10)210
E) χ2=(10−6)26+(30−32)232+(10−12)212
Answer
Answer: D) χ2=(6−10)²/10+(32−30)²/30+(12−10)²/10
Explanation: The chi-square test statistic is calculated as the sum of squared differences between observed and expected counts, divided by the expected counts.
Sourav
