Question

Based on principles of genetics, the population of fruit flies are categorized into four groups: Red eye/Normal Wing (56%), Special Eye/Normal Wing (19%), Red Eye/Vestigial Wing (18%) and Special Eye/Vestigial Wing (7%). Of the 80 fruit flies the class at universiry conducted a genetic experiment on, they came up with the following distribution:

Red eye/Normal Wing – 60​

​Special Eye/Normal Wing – 15

  Red Eye/Vestigial Wing – 2 ​​Special Eye/Vestigial Wing – 3

Use 0.05 level of significance to test the claim that the observed frequencies agree with the proportions that were expected according to the principles of genetics.

Answer 1

let us conside

Ho:the observed frequencies agree with the proportions that were expected according to the principles of genetics

Ha:the observed frequencies do not agree with the proportions that were expected according to the principles of genetics

using minitab>stat>tables

we have

Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: frequency

Using category names in data

Test Contribution
Category Observed Proportion Expected to Chi-Sq
Red eye/Normal Wing 60 0.56 44.8 5.1571
Special Eye/Normal Wing 15 0.19 15.2 0.0026
Red Eye/Vestigial Wing 2 0.18 14.4 10.6778
Special Eye/Vestigial Wing 3 0.07 5.6 1.2071

N DF Chi-Sq P-Value
80 3 17.0447 0.001

sonce p value of chi square stat is 0.001 < 0.05 so we reject Ho and conclude ,the observed frequencies do not agree with the proportions that were expected according to the principles of genetics