Question

case 1: male/female distribution in a population. sample rules of sex determination predict that 50% of normal offspring will be male (xy) and 50% will be female (xx). lets examine a population of mammals. there are 34 hamsters for sale from a breeder. 24 females and 10 males. state the null hypothesis: no difference, no relationship. fill in the chi - square data table. find your degrees of freedom. the degrees of freedom are calculated as one less than the number of possible results in your experiment. degrees of freedom always are found using this formula: # variables - 1. degrees of freedom for this experiment 1. now, use the chi - square table to determine if we accept or reject the null hypothesis. if our chi - square value is equal to or larger than the chi - square value at p value 0.05, we reject our null hypothesis. this means that some other factor (besides chance) is likely playing a role in the distribution of the data that we see. a p value of 0.05 means that only 5% of the time would the data be distributed in this manner due to chance. therefore, we can say with 95% confidence that the data is distributed in this manner due to the experimental variable, not due to chance. lets finish our analysis. is our chi - square value greater than the value at p = 0.05? if so, proceed to the next line. if not, we fail to reject our null that the variation is simply due to chance. with degrees of freedom and percent confidence we our null hypothesis. therefore, something other than is playing a role in the distribution of the data (alternative hypothesis) in this case, it is likely that is playing a role.

Explanation:

Step1: Identify the degrees of freedom

The formula for degrees of freedom is $\text{df}=\text{\# variables}-1$. Here we have 2 variables (male and female), so $\text{df}=2 - 1=1$.

Step2: Determine the decision - making rule

We compare the calculated chi - square value ($\chi^{2}=5.6$) with the critical chi - square value at a significance level of $p = 0.05$ and 1 degree of freedom. Looking up in the chi - square table, the critical value at $p=0.05$ and $\text{df} = 1$ is approximately $3.84$.

Step3: Make a decision

Since our calculated $\chi^{2}=5.6$ is greater than the critical value of $3.84$, we reject the null hypothesis.

Answer:

We reject the null hypothesis.