Q: Which formula is used to calculate the expected frequency in a chi-square test when all outcomes are equally likely?

$\text{Expected frequency} = \frac{\text{Total number of trials}}{\text{Number of categories}}$

Question 1

In an experiment, brown anoles are tested for their preference among brown, green, black, and red backgrounds. The null hypothesis ($H_0$) states that the anoles have no preference. What does the alternative hypothesis ($H_A$) state?

Accepted Answer

Brown anoles have a preference for at least one background color.

Question 2

Given the observed frequencies for brown anoles: brown (45), green (16), black (23), red (16), and expected frequencies of 25 for each, calculate the chi-square ($\chi^2$) value for the brown background. Use the formula $\chi^2 = \sum \frac{(O - E)^2}{E}$.

Accepted Answer

$\frac{(45-25)^2}{25} = 16$

Question 3

If the calculated $\chi^2$ value for the experiment is 28.28 and the degrees of freedom ($df$) is 3, what can you conclude if the critical value for $p = 0.05$ is 7.81?

Accepted Answer

Reject the null hypothesis; the result is statistically significant.

Question 4

What does a p-value less than 0.05 indicate in the context of hypothesis testing?

Accepted Answer

There is strong evidence against the null hypothesis.

Question 5

If the degrees of freedom ($df$) for a chi-square test is calculated as the number of categories minus one, what is $df$ for an experiment with 4 background colors?

Accepted Answer

$4 - 1 = 3$

Question 6

Which of the following best describes the null hypothesis ($H_0$) in the brown anole background preference experiment?

Accepted Answer

Brown anoles have no preference for any background color.

Question 7

If you increase the sample size in a chi-square test, what generally happens to the p-value, assuming the observed effect remains the same?

Accepted Answer

The p-value gets smaller, making it more likely to reject the null hypothesis.

Question 8

A student calculates a $\chi^2$ value of 17.05 for an experiment with 5 degrees of freedom. Is the p-value less than 0.05?

Accepted Answer

Yes, the p-value is less than 0.05.

Question 9

Which statement is true about the relationship between the $\chi^2$ value and the p-value in hypothesis testing?

Accepted Answer

As the $\chi^2$ value increases, the p-value decreases.

Question 10

If the observed frequencies in a chi-square test are very close to the expected frequencies, what is most likely true about the p-value?

Accepted Answer

The p-value will be high, indicating no significant difference.

Question 11

In the context of the experiment, what does it mean if you 'reject the null hypothesis'?

Accepted Answer

There is evidence that brown anoles have a preference for background color.

Question 12

Which formula is used to calculate the expected frequency in a chi-square test when all outcomes are equally likely?

Accepted Answer

$	ext{Expected frequency} = \frac{	ext{Total number of trials}}{	ext{Number of categories}}$

Question 13

A researcher wants to test if a fertilizer affects plant growth. Which result would support the claim that the fertilizer has an effect?

Accepted Answer

You reject the null hypothesis.

Question 14

If you conduct a chi-square test with 7 degrees of freedom and calculate a $\chi^2$ value of 17.05, is the p-value less than 0.05?

Accepted Answer

Yes, the p-value is less than 0.05.

Question 15

What is the primary purpose of using a chi-square test in biological experiments?

Accepted Answer

To determine if observed frequencies differ significantly from expected frequencies.

Question 16

If the calculated p-value from your experiment is 0.03, what should you conclude if your significance level ($\alpha$) is 0.05?

Accepted Answer

Reject the null hypothesis.

Question 17

Which of the following is a common misconception about p-values?

Accepted Answer

A p-value less than 0.05 proves the alternative hypothesis is true.

Question 18

In a chi-square test, which scenario would most likely result in a significant result?

Accepted Answer

Observed frequencies are very different from expected frequencies.

Question 19

If the null hypothesis is true, what should be the relationship between observed and expected frequencies?

Accepted Answer

Observed frequencies should be close to expected frequencies.

Question 20

Which of the following best describes statistical significance in the context of biological experiments?

Accepted Answer

The observed results are unlikely to have occurred by chance alone.

Statistical Analysis in Biology: Hypothesis Testing and Chi-Square Applications

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