Suppose that Max is a climate change scientist and butterfly enthusiast. In Max's locale, the mean summer temperature over the last ten years was higher than it was in the previous ten years. Max wonders if the size of adult male monarch butterflies has changed with the temperature difference. He knows that in his locale, historically, the mean rear wing length of adult male monarchs was 38.3 mm. He collects a random sample of ?n adult male monarchs to compare to the historical average. His sample data is shown in the given stem-and-leaf plot, where the stem unit is mm and the leaf unit is tenths of a mm.35 I 1 236 I 5 6 7 837 I 0 1 2 3 5 6 838 I 0 2 4 4 8 939 I 3 5Leaf Unit = 0.1From experience, Max knows that the rear wing length of monarch butterflies is normally distributed. He decides to use a t-test with a significance level of α = 0.05 to test the null hypothesis, ?0 : ?=38.3against the alternative hypothesis, ?1 : ? ≠ 38.3, where μ is the population mean.If the requirements for a t-test have not been met, only state the test decision and conclusion. Otherwise, find the mean, standard deviation, t-statistic, ?-value,P-value, and state the test decision and conclusion. ## Educational Website Content: Decision and Conclusion of Max's Test### Instruction:Finally, state the decision and conclusion of Max's test.### Completion Task:Max ________________ decision ________________ the ________________. The conclusion is that ________________ the current mean wing size of adult male monarch butterflies ________________.### Answer Bank:- should make the- null hypothesis- is less than 38.3 mm- to reject- to fail to reject- there is sufficient evidence that- is equal to 38.3 mm- alternative hypothesis- cannot make a- there is insufficient evidence that- because the requirements have not been met- is greater than 38.3 mm- no conclusion can be made about- is different than 38.3 mm- about### Diagram Explanation:The image contains blanks to be filled using an answer bank provided below it. The answer bank consists of various statements and phrases related to statistical hypothesis testing. The goal is to craft a coherent conclusion using the elements from the answer bank. **Exercise: Statistical Analysis of Max's Sample**1. **Compute the Mean:** - First, compute the mean, $ \bar{x} $, of Max's sample. Report your answer with two decimals of precision. - \[ \bar{x} = \boxed{\phantom{00}} \text{ mm} \]2. **Compute the Sample Standard Deviation:** - Then, compute the sample standard deviation, $ s $. Report your answer with two decimals of precision. - \[ s = \boxed{\phantom{00}} \text{ mm} \]3. **Compute the t-Statistic:** - Next, compute the $ t $-statistic of the test. Report your answer with three decimals of precision. - \[ t\text{-statistic} = \boxed{\phantom{000}} \]4. **Calculate the P-Value:** - Then, use software to calculate the $ P $-value for the test. Report your answer with three decimals of precision. - \[ P\text{-value} = \boxed{\phantom{000}} \]

Name: Suppose that Max is a climate change scientist and butterfly enthusias
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Description: Suppose that Max is a climate change scientist and butterfly enthusiast. In Max's locale, the mean summer temperature over the last ten years was higher than it was in the previous ten years. Max wonders if the size of adult male monarch butterflies

The distribution is normal and the population standard deviation is unknown so the t distribution…

Suppose that Max is a climate change scientist and butterfly enthusiast. In Max's locale, the mean summer temperature over the last ten years was higher than it was in the previous ten years. Max wonders if the size of adult male monarch butterflies has changed with the temperature difference. He knows that in his locale, historically, the mean rear wing length of adult male monarchs was 38.3 mm. He collects a random sample of ?n adult male monarchs to compare to the historical average. His sample data is shown in the given stem-and-leaf plot, where the stem unit is mm and the leaf unit is tenths of a mm. 35 I 1 2 36 I 5 6 7 8 37 I 0 1 2 3 5 6 8 38 I 0 2 4 4 8 9 39 I 3 5 Leaf Unit = 0.1 From experience, Max knows that the rear wing length of monarch butterflies is normally distributed. He decides to use a t-test with a significance level of α = 0.05 to test the null hypothesis, ?0 : ?=38.3against the alternative hypothesis, ?1 : ? ≠ 38.3, where μ is the population mean. If the requirements for a t-test have not been met, only state the test decision and conclusion. Otherwise, find the mean, standard deviation, t-statistic, ?-value,P-value, and state the test decision and conclusion.

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Suppose that Max is a climate change scientist and butterfly enthusiast. In Max's locale, the mean summer temperature over the last ten years was higher than it was in the previous ten years. Max wonders if the size of adult male monarch butterflies has changed with the temperature difference. He knows that in his locale, historically, the mean rear wing length of adult male monarchs was 38.3 mm. He collects a random sample of ?n adult male monarchs to compare to the historical average. His sample data is shown in the given stem-and-leaf plot, where the stem unit is mm and the leaf unit is tenths of a mm.

35 I 1 2

36 I 5 6 7 8

37 I 0 1 2 3 5 6 8

38 I 0 2 4 4 8 9

39 I 3 5

Leaf Unit = 0.1

From experience, Max knows that the rear wing length of monarch butterflies is normally distributed. He decides to use a t-test with a significance level of α = 0.05 to test the null hypothesis, ?0 : ?=38.3against the alternative hypothesis, ?1 : ? ≠ 38.3, where μ is the population mean.

If the requirements for a t-test have not been met, only state the test decision and conclusion. Otherwise, find the mean, standard deviation, t-statistic, ?-value,P-value, and state the test decision and conclusion.

## Educational Website Content: Decision and Conclusion of Max's Test

### Instruction:
Finally, state the decision and conclusion of Max's test.

### Completion Task:
Max ________________ decision ________________ the ________________. The conclusion is that ________________ the current mean wing size of adult male monarch butterflies ________________.

### Answer Bank:
- should make the
- null hypothesis
- is less than 38.3 mm
- to reject
- to fail to reject
- there is sufficient evidence that
- is equal to 38.3 mm
- alternative hypothesis
- cannot make a
- there is insufficient evidence that
- because the requirements have not been met
- is greater than 38.3 mm
- no conclusion can be made about
- is different than 38.3 mm
- about

### Diagram Explanation:
The image contains blanks to be filled using an answer bank provided below it. The answer bank consists of various statements and phrases related to statistical hypothesis testing. The goal is to craft a coherent conclusion using the elements from the answer bank.

**Exercise: Statistical Analysis of Max's Sample**

1. **Compute the Mean:**
- First, compute the mean, $ \bar{x} $, of Max's sample. Report your answer with two decimals of precision.
- \[
\bar{x} = \boxed{\phantom{00}} \text{ mm}
\]

2. **Compute the Sample Standard Deviation:**
- Then, compute the sample standard deviation, $ s $. Report your answer with two decimals of precision.
- \[
s = \boxed{\phantom{00}} \text{ mm}
\]

3. **Compute the t-Statistic:**
- Next, compute the $ t $-statistic of the test. Report your answer with three decimals of precision.
- \[
t\text{-statistic} = \boxed{\phantom{000}}
\]

4. **Calculate the P-Value:**
- Then, use software to calculate the $ P $-value for the test. Report your answer with three decimals of precision.
- \[
P\text{-value} = \boxed{\phantom{000}}
\]

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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