Chapter 10: Q. 9 (page 446)

Cottonmouth Litter Size. Refer to Problem 8. Find a $98 %$ confidence interval for the difference between the mean litter sizes of cottonmouths in Florida and Virginia. Interpret your result.

Short Answer

Expert verified

Yes

Step by step solution

Given Information

To calculate at $98 %$ significance level, the difference between the mean litter sizes of cottonmouths in Florida and Virginia.

Explanation

As the given data is normally distributed and the given population standard deviations are not equal, the unpooled t-test can be used as follows:

$H_{0} : μ_{1} = μ_{2}$

$H_{α} : μ_{1} < μ_{2}$

After this, calculate the degrees of freedom

Δ = \frac{{(\frac{s_{1}^{2}}{n_{1}} + \frac{{\frac{2}{2}}_{2}^{n_{2}}}{})}^{2}}{\frac{{(\frac{s_{1}^{2}}{n_{1}})}^{2}}{n_{1} - 1} + \frac{{(\frac{z_{2}^{2}}{n_{2}})}^{2}}{n_{2} - 1}} = \frac{{(\frac{(1.59)^{2}}{24} + \frac{(2.68)^{2}}{44})}^{2}}{\frac{{(\frac{(1.59)^{2}}{24})}^{2}}{24 - 1} + \frac{{(\frac{(2.68)^{2}}{44})}^{2}}{44 - 1}} \approx 65

Now, determine $t_{\frac{a}{2}}$ with $d f = 65$

t_{0.01} = 2.385

The confidence interval's endpoints for $μ_{1} - μ_{2}$ can be calculated as:

$({\bar{x}}_{1} - {\bar{x}}_{2}) - t_{\frac{a}{2}} \times \sqrt{\frac{s_{1}^{2}}{n_{1}} + \frac{s_{2}^{2}}{n_{2}}} = (5.46 - 7.59) - 2.385 \times \sqrt{\frac{(1.59)^{2}}{24} + \frac{(2.68)^{2}}{44}} = - 3.366$

$({\bar{x}}_{1} - {\bar{x}}_{2}) + t_{\frac{a}{2}} \times \sqrt{\frac{s_{1}^{2}}{n_{1}} + \frac{s_{2}^{2}}{n_{2}}} = (5.46 - 7.59) + 2.385 \times \sqrt{\frac{(1.59)^{2}}{24} + \frac{(2.68)^{2}}{44}} = - 0.894$

It can be said with $98 %$ confidence that the no: of a young per litter of cottonmouths in Florida is between $0.894$ and $3.366$ less than in Virginia.

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Cottonmouth Litter Size. Refer to Problem 8. Find a $98 %$ confidence interval for the difference between the mean litter sizes of cottonmouths in Florida and Virginia. Interpret your result.

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Cottonmouth Litter Size. Refer to Problem 8. Find a 98%confidence interval for the difference between the mean litter sizes of cottonmouths in Florida and Virginia. Interpret your result.

Short Answer

Step by step solution

Given Information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

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Calculus

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

Cottonmouth Litter Size. Refer to Problem 8. Find a $98 %$ confidence interval for the difference between the mean litter sizes of cottonmouths in Florida and Virginia. Interpret your result.