A study was performed to look at the preference of different...

A study was performed to look at the preference of different species of birds for different types of sunflower seeds. Two bird feeders were set up with different types of sunflower seeds, one with a black oil seed and one with a striped seed. The bird feeders were observed for a 1 -hour period for each of 12 days over a 1 -month period. The number of birds of different species who ate seeds from a specific bird feeder was counted for each bird feeder for each of a number of species of birds. (The data for this problem were supplied by David Rosner.) On the first day of testing, 1 titmouse ate the black oil seeds and 4 titmice ate the striped seeds. Of the goldfinches, 19 ate the black oil seeds and 5 ate the striped seeds. Implement the test in Problem $10.74,$ and report a $p$ -value.

A study was performed to look at the preference of different species of birds for different types of sunflower seeds. Two bird feeders were set up with different types of sunflower seeds, one with a black oil seed and one with a striped seed. The bird feeders were observed for a 1 -hour period for each of 12 days over a 1 -month period. The number of birds of different species who ate seeds from a specific bird feeder was counted for each bird feeder for each of a number of species of birds. (The data for this problem were supplied by David Rosner.)
On the first day of testing, 1 titmouse ate the black oil seeds and 4 titmice ate the striped seeds. Of the goldfinches, 19 ate the black oil seeds and 5 ate the striped seeds.
Implement the test in Problem $10.74,$ and report a $p$ -value.

Key Concepts

Experimental Design

Experimental design involves planning a study so that the data obtained can be analyzed to yield valid and objective conclusions. In observational studies like the one described, key elements include the selection of different conditions (different seed types), repeated measures over multiple days, and careful recording of frequency data. A well-structured experimental design helps in reducing bias, controlling for confounding variables, and ensuring that the results are statistically sound.

Contingency Table

A contingency table is a type of table in a matrix format that displays the frequency distribution of variables. It is used to summarize the relationship between several categorical variables by showing counts of observations that fall into each combination of categories, such as the counts of birds choosing different seed types. This table forms the basis for many statistical tests, including the chi-square test of independence.

Chi-Square Test of Independence

The chi-square test of independence is a statistical procedure used to determine whether there is a significant association between two categorical variables. It compares the observed frequencies in each cell of the contingency table to the frequencies expected under the assumption of independence. A large chi-square statistic indicates a departure from the null hypothesis, suggesting that the variables, such as bird species and seed type preference, are not independent.

Hypothesis Testing

Hypothesis testing is a systematic method used in statistics to make inferences about a population based on sample data. In the context of this type of study, it involves setting up a null hypothesis that assumes no relationship between the variables (for example, no difference in seed preference among bird species) and an alternative hypothesis that suggests a relationship exists. The test then determines whether the observed data provide enough evidence to reject the null hypothesis.

P-Value

The p-value is a measure used in hypothesis testing that quantifies the probability of observing an effect as extreme as, or more extreme than, the one found in the sample data if the null hypothesis were true. A low p-value indicates that such an extreme result is unlikely under the null hypothesis, thereby providing evidence against it. In studies like this, reporting a p-value helps to assess the statistical significance of the relationship between categorical variables.

Transcript

00:01 In question seven, it says researchers studied the behavior of birds that were searching for seeds and insects in oregon forest.

00:07 It tells us the percentage of trees that were douglas firs, that were pines, and that were other types of trees.

00:14 And then they randomly selected a time during the day where the researchers observed 156 red -breasted nut hatches.

00:21 70 were seen in furs, 79 were seen in pines, and seven were seen in other trees.

00:25 Do the data suggest that nut hatches prefer particular types of trees when they're searching for seeds and insects, carry out a kai squared goodness of fit test to help answer this question.

00:34 So if we're going to carry out a test, we need to do the four steps, state plan do conclude.

00:40 So our first thing is state here.

00:42 So what do we want to know? we want to test the following hypotheses at a significance level of 5%.

00:48 So the null hypothesis is that nut hatches do not prefer a particular type of tree.

00:54 And the alternative hypothesis is that nut hatches do prefer a particular type of tree.

01:00 You can also see this written.

01:02 Differently.

01:03 If you look in the answer key in the back of your textbook, i wanted to show it this way because you may not have seen this, this method, but either one is perfectly okay.

01:12 So the plan, if the conditions are met, we will perform a k -squared goodness -of -hit test...

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