## Related questions with answers

Researchers studied the behavior of birds that were searching for seeds and insects in an Oregon forest. In this forest, 54% of the trees were Douglas firs, 40% were ponderosa pines, and 6% were other types of trees. At a randomly selected time during the day, the researchers observed 156 red-breasted nuthatches: 70 were seen in Douglas firs, 79 in ponderosa pines, and 7 in other types of trees. Do these data provide convincing evidence that nuthatches prefer particular types of trees when they're searching for seeds and insects?

Solution

VerifiedThe null hypothesis states that the population proportions are equal to the mentioned proportions:

$H_0:p_1=0.54, p_2=0.4, p_3=0.06$

The alternative hypothesis states the opposite of the null hypothesis:

$H_a:\text{At least one of the }p_i\text{'s is different.}$

Determine the observed frequencies $O$.

The expected frequencies $E$ are the product of the sample size $n$ and the probabilities $p_i$.

The chi-square subtotals are the squared differences between the observed and expected frequencies, divided by the expected frequency.

$\chi^2_{sub}=\dfrac{(O-E)^2}{E}$

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