Python eggs How is the hatching of water python eggs...

Python eggs How is the hatching of water python eggs influenced by the temperature of the snake’s nest? Researchers randomly assigned newly laid eggs to one of three water temperatures: hot, neutral, or cold. Hot duplicates the extra warmth provided by the mother python, and cold duplicates the absence of the mother. Here are the data on the number of eggs and the number that hatched:17 $\begin{array}{lll}{\text { Cold }} & {27} & {16} \\ {\text { Neutral }} & {56} & {38} \\ {\text { Hot }} & {104} & {75} \\ \hline\end{array}$ (a) Make a two-way table of temperature by outcome (hatched or not). Calculate the proportion of eggs in each group that hatched. The researchers believed that eggs would not hatch in cold water. Do the data support that belief? (b) Are the differences between the three groups statistically significant? Give appropriate evidence to support your answer.

Python eggs How is the hatching of water python eggs influenced by the temperature of the snake’s nest? Researchers randomly assigned newly laid eggs to one of three water temperatures: hot, neutral, or cold. Hot duplicates the extra warmth provided by the mother python, and cold duplicates the absence of the mother. Here are the data on the number of eggs and the number that hatched:17
$\begin{array}{lll}{\text { Cold }} & {27} & {16} \\ {\text { Neutral }} & {56} & {38} \\ {\text { Hot }} & {104} & {75} \\ \hline\end{array}$
(a) Make a two-way table of temperature by outcome (hatched or not). Calculate the proportion of eggs in each group that hatched. The researchers believed that eggs would not hatch in cold water. Do the data support that belief?
(b) Are the differences between the three groups statistically significant? Give appropriate evidence to support your answer.

Key Concepts

Statistical Significance

Statistical significance is a measure that indicates whether the observed differences or associations in data are unlikely to have occurred by chance alone. It is typically assessed using a p-value, and a result is usually considered statistically significant if the p-value falls below a predetermined threshold.

Experimental Design

Experimental design involves planning how to collect and assign data in a study to ensure that the research question is addressed effectively while minimizing bias. Techniques such as random assignment of subjects to different treatment groups are essential to establish causality and ensure that comparisons between groups are valid.

Proportions

Proportions describe the relative frequency of an event occurring within a specific group compared to the total observations in that group. They provide a normalized measure to compare groups of different sizes and help in identifying patterns or differences across categories.

Contingency Table

A contingency table, also known as a two?way table, organizes categorical data into rows and columns to show the distribution of responses across different groups or conditions. This table format is essential for visualizing the relationship between two categorical variables and serves as a foundation for further statistical testing.

Chi-Square Test

The Chi-Square Test is a statistical method used to examine the association between two categorical variables by comparing observed frequencies in a contingency table to expected frequencies under the assumption of independence. This test helps determine if the differences seen across groups are statistically significant.

Transcript

00:05 All right, the problem asks us to first make a two -way table by outcome, so whether they hatched or not, and then are the differences in the group statistically significant? so i went ahead and just copied the table that they give you in the book first, because we're going to need that, obviously.

00:22 And that's all i've done so far.

00:24 Now, when we're making two -way table, all we need to is take the table they gave us, and we need to add two more sections.

00:31 We simply need to add a total section.

00:41 And that's really the only thing.

00:42 If we have this set of data, all we need to do is add a total because if we're going to do a kai score statistic, we're going to need to know the sum of columns and rows.

00:50 So if i count totals, it looks like i have 27 in the first row, 56 in the second, 104 in the last.

01:02 That's a total of 187, then 129, and then 58.

01:10 And wow, that is a bad 58.

01:12 I'll try to write a little better.

01:16 58.

01:16 All righty.

01:19 So what we have here is now all the totals.

01:23 Note that this row in red should equal 187 just as this column does, because we should have a 187 should be the total of all, the total number of observations or trials.

01:39 And then it says, make a tweet table outcome, then it asked us to, i guess i didn't write all the instructions.

01:47 It asked us to find the, it wanted us to also, so part a, i guess i didn't write all this down.

01:54 So make it too, we too, we too outcome.

01:55 Then it wanted us to find the conditional, find conditional distribution.

02:10 Does this support theory? so, okay, so i guess i didn't write the whole question down.

02:23 So the next thing you need to do is find the conditional distribution.

02:28 With regards to their respective categories of temperature.

02:34 And i'm just gonna add that to this table i already have, just because it's kind of organized.

02:39 If i think about this row of cold, this cold row, 16 divided by, 16 divided by 27, so 16 divided by 27.

02:55 That's gonna tell me that 16 is point, 0 .593.

03:02 And that means it's a complement is 0 .407.

03:05 So in terms of the cold batch, 60 % hatched.

03:12 All right.

03:13 Now let's go with the neutral batch.

03:15 So again, i'm just taking this number and dividing it by that number over there.

03:19 So 0 .679 .321, 0 .721 and 0 .274.

03:34 So what do we do here? two -way table, conditional distribution, does this support theory? all right.

03:42 So the theory was that the mother being present would affect the birth, and that's why they had hot, because hot would replicate the temperature of a mother being by to give warmth to the eggs.

03:55 And so the conditional distribution supports the claim that a mother's presence affects hatching rates and we see that cold was only 60 % and hot was 72 % so there is this linear difference about temperature that we see happening here.

04:51 Well, i mean, not almost linear, i should say.

04:53 But the point is we see this increasing rate, which supports the idea that there is a relationship between mother's presence and the burling of the eggs.

05:04 Next, we are supposed to say, are the differences in the groups statistically significant? okay, well, did that? are the differences in the groups significant conditions? to do that, it's basically saying let's do a kai square test.

05:21 Now we do kind of square test, then there's a couple things we need to check.

05:23 So this is now part b.

05:31 So we have, first off, our null hypothesis, there is no difference in the proportion of eggs that hatch based on water temperature.

06:14 Okay, this is a null hypothesis.

06:17 Alternate hypothesis is simply that there is a difference in the proportion of the hatch paste and water temperature.

06:37 So what i'm saying is there is a difference.

06:39 Then you just copy and paste all that right there.

06:50 I don't feel like writing it twice.

06:51 So just copy and paste.

06:53 Okay.

06:53 So those are two, our two hypotheses.

06:55 And then what we need to do is we already have, sorry, we already have a table.

07:06 This is our observed outcomes is what this table is what this table is we need is we need a table of expected outcomes oh i'm going to head of myself before we do that we are going to do that before we do that we need to check the conditions that make a kai square test viable okay so oh that's not what i wanted okay conditions okay, first off, is this study random? it says that the, in the problem, that the data came, it says in the problem that the data came from a randomized experiment.

08:24 So it is indeed random.

08:26 Those are terrible check marks.

08:28 All right.

08:29 And then, i'm just going to raise this, i'll rewrite it in a minute, and then we needed to check, there's the, oh, i wrote it down, what's the official name for it? the large sample size rule or the, the basically expected outcome rule, and that is that expected counts need to be greater than or equal to five...

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