Generally, large values of are highly improbable when the null hypothesis is true. (Note that if the expected and observed values are exactly the same, takes on a value of zero). Statisticians have computed the exact probabilities of obtaining different values of under a true null hypothesis. For the example given above, the probability of obtaining a 2 of 3.84 (known as a critical value) or greater when the null hypothesis is true is less than 0.05 (in other words, less than 5% of the time). If the calculated value of is greater than this critical value, the null hypothesis is rejected in favor of the alternative. In the next class meeting you will work in groups of four to discuss the use of statistical procedures in hypothesis testing. Each person in the group will act as the 'facilitator' for one question, leading the group discussion, promoting input from each of the other students (who will be acting as 'discussants') and formalizing the group response. In the role of a discussant, students provide their knowledge, experience and perspectives, compare and contrast the inputs of other members of the group and collaborate in the formulation of the group response. At the end of the activity, you may be called on to present your group's answers to one of the questions (not necessarily the one you were the facilitator for). You will act as both a facilitator and a discussant in the activity. Identification/Observation 1. How is a statistical hypothesis best defined? Statistical hypothesis is testing inferences that would be predicted based on data that is given from a population. 2. According to the reading, what do large values of typically lead to? I 3. Based on the value obtained from the rhino data, would you reject or fail to reject the null hypothesis that the sex ratio is 1:1? Explain your reasoning
Generally, large values of are highly improbable when the null hypothesis is true. (Note that if the expected and observed values are exactly the same, takes on a value of zero). Statisticians have computed the exact probabilities of obtaining different values of under a true null hypothesis. For the example given above, the probability of obtaining a 2 of 3.84 (known as a critical value) or greater when the null hypothesis is true is less than 0.05 (in other words, less than 5% of the time). If the calculated value of is greater than this critical value, the null hypothesis is rejected in favor of the alternative. In the next class meeting you will work in groups of four to discuss the use of statistical procedures in hypothesis testing. Each person in the group will act as the 'facilitator' for one question, leading the group discussion, promoting input from each of the other students (who will be acting as 'discussants') and formalizing the group response. In the role of a discussant, students provide their knowledge, experience and perspectives, compare and contrast the inputs of other members of the group and collaborate in the formulation of the group response. At the end of the activity, you may be called on to present your group's answers to one of the questions (not necessarily the one you were the facilitator for). You will act as both a facilitator and a discussant in the activity. Identification/Observation 1. How is a statistical hypothesis best defined? Statistical hypothesis is testing inferences that would be predicted based on data that is given from a population. 2. According to the reading, what do large values of typically lead to? I 3. Based on the value obtained from the rhino data, would you reject or fail to reject the null hypothesis that the sex ratio is 1:1? Explain your reasoning
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
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Generally, large values of are highly improbable when the null hypothesis is true. (Note that if the
expected and observed values are exactly the same, takes on a value of zero). Statisticians have
computed the exact probabilities of obtaining different values of x under a true null hypothesis. For
the example given above, the probability of obtaining a of 3.84 (known as a critical value) or greater
when the null hypothesis is true is less than 0.05 (in other words, less than 5% of the time). If the
calculated value of is greater than this critical value, the null hypothesis is rejected in favor of the
alternative.
1
AA
DII
(
In the next class meeting you will work in groups of four to discuss the use of statistical
procedures in hypothesis testing. Each person in the group will act as the 'facilitator' for one question,
leading the group discussion, promoting input from each of the other students (who will be acting as
'discussants') and formalizing the group response. In the role of a discussant, students provide their
knowledge, experience and perspectives, compare and contrast the inputs of other members of the
and collaborate in the formulation of the group response. At the end of the activity, you may be
called on to present your group's answers to one of the questions (not necessarily the one you were the
facilitator for). You will act as both a facilitator and a discussant in the activity.
group
9
Identification/Observation
1. How is a statistical hypothesis best defined?
Statistical hypothesis is testing inferences that would be predicted based on data that is given from a
population.
2. According to the reading, what do large values of
typically lead to?
3. Based on the value obtained from the rhino data, would you reject or fail to reject the null
hypothesis that the sex ratio is 1:1? Explain your reasoning,
Formulation of a plan
4. Imagine that you are interested in testing whether or not a trait segregates in a 9:3:3:1 phenotypic
ratio, Formulate your null and alternative hypotheses for this scenario. How did you arrive at this
determination?
5. Suppose the test statistic had been computed as = 1.76. Based on this value, what would our
biologist do?
O
Name
Calculation/Data Collection
6. Suppose that you expect a 2:1 male female sex ratio in a certain insect population. You collect 90
insects at random of which 70 are males and 20 are females. What is the expected number of males
under your null hypothesis?
7. Calculate the chi-square value for the example above.
=.
Paragraph
Application/Analysis
8. Based on the x2 value calculated in question 7, would you reject or fail to reject the null hypothesis
in question 6? Explain your reasoning.
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Generally, large values of are highly improbable when the null hypothesis is true. (Note that if the
expected and observed values are exactly the same, takes on a value of zero). Statisticians have
computed the exact probabilities of obtaining different values of x under a true null hypothesis. For
the example given above, the probability of obtaining a of 3.84 (known as a critical value) or greater
when the null hypothesis is true is less than 0.05 (in other words, less than 5% of the time). If the
calculated value of is greater than this critical value, the null hypothesis is rejected in favor of the
alternative.
1
AA
DII
(
In the next class meeting you will work in groups of four to discuss the use of statistical
procedures in hypothesis testing. Each person in the group will act as the 'facilitator' for one question,
leading the group discussion, promoting input from each of the other students (who will be acting as
'discussants') and formalizing the group response. In the role of a discussant, students provide their
knowledge, experience and perspectives, compare and contrast the inputs of other members of the
and collaborate in the formulation of the group response. At the end of the activity, you may be
called on to present your group's answers to one of the questions (not necessarily the one you were the
facilitator for). You will act as both a facilitator and a discussant in the activity.
group
9
Identification/Observation
1. How is a statistical hypothesis best defined?
Statistical hypothesis is testing inferences that would be predicted based on data that is given from a
population.
2. According to the reading, what do large values of
typically lead to?
3. Based on the value obtained from the rhino data, would you reject or fail to reject the null
hypothesis that the sex ratio is 1:1? Explain your reasoning,
Formulation of a plan
4. Imagine that you are interested in testing whether or not a trait segregates in a 9:3:3:1 phenotypic
ratio, Formulate your null and alternative hypotheses for this scenario. How did you arrive at this
determination?
5. Suppose the test statistic had been computed as = 1.76. Based on this value, what would our
biologist do?
O
Name
Calculation/Data Collection
6. Suppose that you expect a 2:1 male female sex ratio in a certain insect population. You collect 90
insects at random of which 70 are males and 20 are females. What is the expected number of males
under your null hypothesis?
7. Calculate the chi-square value for the example above.
=.
Paragraph
Application/Analysis
8. Based on the x2 value calculated in question 7, would you reject or fail to reject the null hypothesis
in question 6? Explain your reasoning.
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Hypothesis Testing and Data Analysis (Scenario)
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One method that biologists use to conduct research is by collecting experimental data through
statistical hypothesis testing. Statistical hypotheses are testable predictions about what we would
expect to observe under a given set of conditions. For example, a conservation biologist might
hypothesize that the sex-ratio of adult black rhinos in Kruger national park is 1:1 (the number of adult
males and females is equivalent). This seems sensible if male and females have about the same chances
of being born and surviving to adulthood. But how would she go about testing the validity of this
hypothesis? The best approach would be to obtain the exact sex ratio of the entire rhino population of
the park, and see if it is indeed 1:1. This is impossible, however, as the park is very large, and even
adult rhinos are very good at hiding from nosy biologists. The next best solution is to obtain a sample
count of the rhinos, and from this extrapolate to the entire population. Suppose our biologist conducts
an aerial survey of adult rhinos in the park, and at the end of a week has counted 135 males and 165
females. The sex ratio of the rhinos in her sample is clearly different from 1:1, but can she infer that the
same is true for the population in the park?
(
To put this in perspective, imagine two buckets, each filled with 100,000 red and white marbles.
In one bucket, the ratio of red to white marbles is exactly 1:1, and in the other it is not 1:1. Imagine
further that I hand you a sample of 300 marbles drawn randomly from one of the two buckets (I don't
tell you which one), and that 133 of the marbles are red and 167 are white. How confident are you that
the sample I handed you did not come from the bucket in which the true ratio of red to white marbles is
truly1:1? Would you wager $10,000 on your ability to make the correct decision?
9
Fortunately, statisticians have devised methods that allow us calculate probabilities upon which
we can base our decisions. The application of these methods to hypothesis testing is made possible in
the form of inferential statistics. Before we decide on an appropriate statistical test for our rhino
experiment, we must formalize a set of mutually exclusive hypotheses. Since our biological knowledge
leads us to predict a 1:1 sex ratio, we state our null hypothesis (Ho) as the sex ratio is 1:1. Since the
ratio is either 1:1 or something else, our alternative hypothesis (HA) is simply that the sex ratio it is
not 1:1. In the example above, our sample of observations consists of aerial counts of 300 adult rhinos.
Hence, if the null hypothesis is correct, we would expect our count to consist of exactly 150 males and
150 females. Our observed sex ratio, however, is 133 males and 167 females. The key question is this:
what is the probability that we could have gotten these numbers if our null hypothesis is correct?
Activity Hypothesis Testing (EQS) Onlin...
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Editing
While there are many different statistical procedures, these data lend themselves to analysis by
the chi-square goodness-of-fit test. The chi-square goodness-of-fit test is a statistical procedure that is
useful in finding out if the observed value of a given phenomena is significantly different from the
expected value. The test statistic, (chi-square), is computed as: x² = E(observed-
expected)²/expected.
For the example above, we can compute a value of x = (133-150)²/150+ (167-150)/150 = 3.85.
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Hypothesis Testing and Data Analysis (Scenario)
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***
One method that biologists use to conduct research is by collecting experimental data through
statistical hypothesis testing. Statistical hypotheses are testable predictions about what we would
expect to observe under a given set of conditions. For example, a conservation biologist might
hypothesize that the sex-ratio of adult black rhinos in Kruger national park is 1:1 (the number of adult
males and females is equivalent). This seems sensible if male and females have about the same chances
of being born and surviving to adulthood. But how would she go about testing the validity of this
hypothesis? The best approach would be to obtain the exact sex ratio of the entire rhino population of
the park, and see if it is indeed 1:1. This is impossible, however, as the park is very large, and even
adult rhinos are very good at hiding from nosy biologists. The next best solution is to obtain a sample
count of the rhinos, and from this extrapolate to the entire population. Suppose our biologist conducts
an aerial survey of adult rhinos in the park, and at the end of a week has counted 135 males and 165
females. The sex ratio of the rhinos in her sample is clearly different from 1:1, but can she infer that the
same is true for the population in the park?
(
To put this in perspective, imagine two buckets, each filled with 100,000 red and white marbles.
In one bucket, the ratio of red to white marbles is exactly 1:1, and in the other it is not 1:1. Imagine
further that I hand you a sample of 300 marbles drawn randomly from one of the two buckets (I don't
tell you which one), and that 133 of the marbles are red and 167 are white. How confident are you that
the sample I handed you did not come from the bucket in which the true ratio of red to white marbles is
truly1:1? Would you wager $10,000 on your ability to make the correct decision?
9
Fortunately, statisticians have devised methods that allow us calculate probabilities upon which
we can base our decisions. The application of these methods to hypothesis testing is made possible in
the form of inferential statistics. Before we decide on an appropriate statistical test for our rhino
experiment, we must formalize a set of mutually exclusive hypotheses. Since our biological knowledge
leads us to predict a 1:1 sex ratio, we state our null hypothesis (Ho) as the sex ratio is 1:1. Since the
ratio is either 1:1 or something else, our alternative hypothesis (HA) is simply that the sex ratio it is
not 1:1. In the example above, our sample of observations consists of aerial counts of 300 adult rhinos.
Hence, if the null hypothesis is correct, we would expect our count to consist of exactly 150 males and
150 females. Our observed sex ratio, however, is 133 males and 167 females. The key question is this:
what is the probability that we could have gotten these numbers if our null hypothesis is correct?
Activity Hypothesis Testing (EQS) Onlin...
Tell me
Editing
While there are many different statistical procedures, these data lend themselves to analysis by
the chi-square goodness-of-fit test. The chi-square goodness-of-fit test is a statistical procedure that is
useful in finding out if the observed value of a given phenomena is significantly different from the
expected value. The test statistic, (chi-square), is computed as: x² = E(observed-
expected)²/expected.
For the example above, we can compute a value of x = (133-150)²/150+ (167-150)/150 = 3.85.
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Hi! Thank you for the question. Since you have posted a question with multiple subparts, we will provide the solution only to the first three subparts as per our Q&A guidelines. To get the remaining subparts solved, please repost the complete question and mention the subparts to be solved.
In this case, the mentioned paragraph is about Hypothesis Testing and Chi-square test.
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