Question

Calculate the observed frequency and expected frequency of a data set. kaitlin recorded the results for a sample of 536 candies.

Color Counts Sample Proportion ()
Red 123 23%
Yellow 145 27%
Green 64 12%
Orange 129 24%
Purple 75 14%

the candy company claims that the distribution of each color is exactly 20%.
select the observed and expected frequencies for the yellow candies.
a.) observed: 107.2 expected: 14
b.) observed: 145 expected: 107.2
c.) observed: 123 expected: 80.4
d.) observed: 145 expected: 80.4

Answer 1

Observed frequency of yellow candies: 145. Expected frequency, as per the company's claim of 20% distribution: 107.2 correct option is b.

calculate the observed and expected frequencies for the yellow candies

Given:

Total sample size (n) = 536 candies

Observed frequency for yellow candies:

The observed frequency is the number of yellow candies recorded in the sample.

Observed frequency = Number of yellow candies recorded = 145

Expected frequency for yellow candies based on the company's claim of 20% distribution for each color:

The expected frequency is the number of yellow candies expected if the company's claim of a 20% distribution for each color holds true.

Expected frequency = Total sample size × Expected proportion of yellow candies

Expected proportion of yellow candies = 20% = 0.20

Expected frequency = Total sample size × Expected proportion of yellow candies

Expected frequency = 536 × 0.20 = 107.2

Therefore, the calculations show:

Observed frequency for yellow candies: 145

Expected frequency for yellow candies: 107.2