Answer:
The data doesn't provide sufficient evidence that the response to the television show is different for boys and girls
Step-by-step explanation:
We will be conducting a χ²-test of independence where the conditions are:
Expected value is >5 (condition is met)
Random sample (condition is met)
Categorical data (condition is met
Our null and alternate hypotheses are:
H: Observed=Expected
Ha: Observed≠Expected
Our expected values would be:
Not Interested + Boys : (220)(110)/500 = 48.4
Not Interested + Girls : (280)(110)/500 = 61.6
Somewhat Interested + Boys : (220)(205)/500 = 90.2
Somewhat Interested + Girls : (280)(205)/500 = 114.8
Very Interested + Boys: (220)(185)/500 = 81.4
Very Interested + Girls: (280)(185)/500 = 103.6
Now we will use the formula χ² = ∑[(O-E)^2/E] where O is the observed value and E is the expected value:
χ² = (50-48.4)²/48.4 + (60-61.6)²/61.6 + (105-90.2)²/90.2 + (100-114.8)²/114.8 + (65-81.4)²/81.4 + (120-103.6)²/103.6 = 10.3311622159
Our degrees of freedom equates to (r-1)(c-1) where r is the number of rows and c is the number of columns. This means our degrees of freedom is df=(3-1)(2-1)=(2)(1)=2
Now we will find the p-value of our χ² test statistic by calculating χ²cdf(10.3311622159,1e99,2) which equals 0.0057097439 which is our p-value
Assuming a 5% significance level, since 0.0057<0.05, we reject the null hypothesis and conclude that the data doesn't provide evidence that the response to the television show is different for boys and girls. Since we found H: Observed=Expected to be true, that means it's more likely that there's not much of a difference between the observed and expected values.
As this took a lot of work, I would highly appreciate a Brainliest if possible! Thank you, and I hope this explanation was helpful! Comment below if you would like me to explain anything further.
