A random sample of 16 adult male wolves from the Canadian Northwest Territories gave an average weight x1 = 97.4 pounds with estimated sample standard deviation s = 6.6 pounds. Another sample of 23 adult male wolves from Alaska gave an average weight x2 = 89.0 pounds with estimated sample standard deviation s2 = 6.4 pounds. n USE SALT (a) Categorize the problem below according to parameter being estimated, proportion p, mean u, difference of means u1 - 42, or difference of proportions P1 - P2. Then solve the problem. O u1 - 42 O P1- P2 (b) Let uz represent the population mean weight of adult male wolves from the Northwest Territories, and let 42 represent the population mean weight of adult male wolves from Alaska. Find a 95% confidence interval for H1 - 42. (Use 1 decimal place.) lower limit upper limit (c) Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 95% level of confidence, does it appear that the average weight of adult male wolves from the Northwest Territories is greater than that of the Alaska wolves? O Because the interval contains only positive numbers, we can say that Canadian wolves weigh more than Alaskan wolves. O Because the interval contains both positive and negative numbers, we can not say that Canadian wolves weigh more than Alaskan wolves. O We can not make any conclusions using this confidence interval. O Because the interval contains only negative numbers, we can say that Alaskan wolves weigh more than Canadian wolves.
A random sample of 16 adult male wolves from the Canadian Northwest Territories gave an average weight x1 = 97.4 pounds with estimated sample standard deviation s = 6.6 pounds. Another sample of 23 adult male wolves from Alaska gave an average weight x2 = 89.0 pounds with estimated sample standard deviation s2 = 6.4 pounds. n USE SALT (a) Categorize the problem below according to parameter being estimated, proportion p, mean u, difference of means u1 - 42, or difference of proportions P1 - P2. Then solve the problem. O u1 - 42 O P1- P2 (b) Let uz represent the population mean weight of adult male wolves from the Northwest Territories, and let 42 represent the population mean weight of adult male wolves from Alaska. Find a 95% confidence interval for H1 - 42. (Use 1 decimal place.) lower limit upper limit (c) Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 95% level of confidence, does it appear that the average weight of adult male wolves from the Northwest Territories is greater than that of the Alaska wolves? O Because the interval contains only positive numbers, we can say that Canadian wolves weigh more than Alaskan wolves. O Because the interval contains both positive and negative numbers, we can not say that Canadian wolves weigh more than Alaskan wolves. O We can not make any conclusions using this confidence interval. O Because the interval contains only negative numbers, we can say that Alaskan wolves weigh more than Canadian wolves.
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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![### Confidence Interval Calculation for Mean Weights of Adult Male Wolves
**Scenario:**
A random sample of 16 adult male wolves from the Canadian Northwest Territories gave an average weight of \( \bar{x}_1 = 97.4 \) pounds, with an estimated sample standard deviation \( s_1 = 6.6 \) pounds. Another sample of 23 adult male wolves from Alaska gave an average weight of \( \bar{x}_2 = 89.0 \) pounds, with an estimated sample standard deviation \( s_2 = 6.4 \) pounds.
**Instructions:**
Use the data provided to categorize and solve the problem using statistical methods.
**Task (a): Problem Categorization**
- **Categories:**
- [ ] \( p \)
- [ ] \( \mu \)
- [ ] \( \mu_1 - \mu_2 \) (Difference of means)
- [ ] \( p_1 - p_2 \)
**Solution:**
- Select \( \mu_1 - \mu_2 \)
**Task (b): Confidence Interval Calculation**
- **Directions:** Let \( \mu_1 \) represent the population mean weight of adult male wolves from the Northwest Territories, and let \( \mu_2 \) represent the population mean weight of adult male wolves from Alaska. Find a 95% confidence interval for \( \mu_1 - \mu_2 \). (Use 1 decimal place).
- **Formulas and Steps:**
1. Calculate the difference in sample means: \( \bar{x}_1 - \bar{x}_2 \).
2. Use the formula for the confidence interval for the difference in means with unequal variances (Welch's t-interval):
\[
(\bar{x}_1 - \bar{x}_2) \pm t_{\alpha/2} \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}
\]
where:
- \(\bar{x}_1 = 97.4\)
- \(\bar{x}_2 = 89.0\)
- \(s_1 = 6.6\)
- \(s_2 = 6.4\)
- \(n_1 = 16\)
- \(n_2 = 23\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1da81aa5-c0e9-4d6e-87eb-a5febb367169%2F7ba9aade-de5c-434d-924e-125eff854475%2Fguzzzkd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Confidence Interval Calculation for Mean Weights of Adult Male Wolves
**Scenario:**
A random sample of 16 adult male wolves from the Canadian Northwest Territories gave an average weight of \( \bar{x}_1 = 97.4 \) pounds, with an estimated sample standard deviation \( s_1 = 6.6 \) pounds. Another sample of 23 adult male wolves from Alaska gave an average weight of \( \bar{x}_2 = 89.0 \) pounds, with an estimated sample standard deviation \( s_2 = 6.4 \) pounds.
**Instructions:**
Use the data provided to categorize and solve the problem using statistical methods.
**Task (a): Problem Categorization**
- **Categories:**
- [ ] \( p \)
- [ ] \( \mu \)
- [ ] \( \mu_1 - \mu_2 \) (Difference of means)
- [ ] \( p_1 - p_2 \)
**Solution:**
- Select \( \mu_1 - \mu_2 \)
**Task (b): Confidence Interval Calculation**
- **Directions:** Let \( \mu_1 \) represent the population mean weight of adult male wolves from the Northwest Territories, and let \( \mu_2 \) represent the population mean weight of adult male wolves from Alaska. Find a 95% confidence interval for \( \mu_1 - \mu_2 \). (Use 1 decimal place).
- **Formulas and Steps:**
1. Calculate the difference in sample means: \( \bar{x}_1 - \bar{x}_2 \).
2. Use the formula for the confidence interval for the difference in means with unequal variances (Welch's t-interval):
\[
(\bar{x}_1 - \bar{x}_2) \pm t_{\alpha/2} \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}
\]
where:
- \(\bar{x}_1 = 97.4\)
- \(\bar{x}_2 = 89.0\)
- \(s_1 = 6.6\)
- \(s_2 = 6.4\)
- \(n_1 = 16\)
- \(n_2 = 23\
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