An economist is interested in the variability of hourly wages at a production plant. She collects data on 50 hourly wage earners. Use the accompanying Excel Data File for this exercise. Click here for the Excel Data File a. Select the competing hypotheses to test whether the variance of hourly wages exceeds 35($2). O Ho: 0² ≤ 35; HA: 0² > 35 Ho: ² = 35; HA: 0² # 35 HØ: 0²35; HA: 02 < 35 b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) Test statistic c. Find the p-value. O 0.025 s p-value < 0.05 O 0.01 s p-value < 0.025 O 0.05 ≤ p-value < 0.10 O p-value 20.10 O p-value < 0.01 d. At the 5% significance level, does the variance of hourly wages exceed 35($²)? O Do not reject He; we cannot conclude the variance of the hourly wages exceeds 35($²). O Reject He; we cannot conclude the variance of the hourly wages exceeds 35 ($²). O Do not reject Ho; we can conclude the variance of the hourly wages exceeds 35 ($²). O Reject Ho; we can conclude the variance of the hourly wages exceeds 35 ($²).
An economist is interested in the variability of hourly wages at a production plant. She collects data on 50 hourly wage earners. Use the accompanying Excel Data File for this exercise. Click here for the Excel Data File a. Select the competing hypotheses to test whether the variance of hourly wages exceeds 35($2). O Ho: 0² ≤ 35; HA: 0² > 35 Ho: ² = 35; HA: 0² # 35 HØ: 0²35; HA: 02 < 35 b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) Test statistic c. Find the p-value. O 0.025 s p-value < 0.05 O 0.01 s p-value < 0.025 O 0.05 ≤ p-value < 0.10 O p-value 20.10 O p-value < 0.01 d. At the 5% significance level, does the variance of hourly wages exceed 35($²)? O Do not reject He; we cannot conclude the variance of the hourly wages exceeds 35($²). O Reject He; we cannot conclude the variance of the hourly wages exceeds 35 ($²). O Do not reject Ho; we can conclude the variance of the hourly wages exceeds 35 ($²). O Reject Ho; we can conclude the variance of the hourly wages exceeds 35 ($²).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
| Wage | EDUC | EXPER | AGE | Male |
| 37.47 | 11 | 2 | 40 | 1 |
| 21.57 | 4 | 1 | 39 | 0 |
| 14.06 | 4 | 2 | 38 | 0 |
| 24.08 | 5 | 9 | 53 | 1 |
| 27.26 | 6 | 15 | 59 | 1 |
| 26.47 | 6 | 12 | 36 | 1 |
| 14.63 | 9 | 5 | 45 | 0 |
| 21.2 | 4 | 12 | 37 | 0 |
| 28.14 | 5 | 14 | 37 | 1 |
| 28.31 | 11 | 3 | 43 | 1 |
| 16.76 | 8 | 5 | 32 | 0 |
| 22.53 | 9 | 18 | 40 | 1 |
| 24.42 | 7 | 1 | 49 | 1 |
| 15.98 | 4 | 10 | 43 | 0 |
| 15.52 | 1 | 9 | 31 | 0 |
| 33.98 | 9 | 22 | 45 | 0 |
| 38.19 | 11 | 3 | 31 | 1 |
| 22.62 | 4 | 14 | 55 | 0 |
| 17.59 | 6 | 5 | 30 | 1 |
| 17.31 | 9 | 3 | 28 | 0 |
| 21.57 | 6 | 15 | 60 | 1 |
| 20.47 | 4 | 13 | 32 | 0 |
| 15.3 | 4 | 9 | 58 | 1 |
| 15.82 | 5 | 4 | 28 | 0 |
| 16.53 | 6 | 5 | 40 | 1 |
| 16.17 | 6 | 2 | 37 | 0 |
| 26.24 | 4 | 18 | 52 | 1 |
| 19.69 | 6 | 4 | 44 | 0 |
| 15.79 | 6 | 4 | 57 | 0 |
| 17.45 | 9 | 3 | 30 | 1 |
| 17.18 | 5 | 8 | 43 | 0 |
| 17.13 | 7 | 6 | 31 | 1 |
| 13.36 | 4 | 3 | 33 | 0 |
| 15.02 | 6 | 23 | 51 | 1 |
| 17.89 | 4 | 15 | 37 | 0 |
| 15.16 | 4 | 9 | 45 | 0 |
| 16.66 | 6 | 3 | 55 | 0 |
| 17.79 | 5 | 14 | 57 | 0 |
| 35.56 | 9 | 16 | 36 | 1 |
| 20.05 | 4 | 20 | 60 | 1 |
| 11.05 | 4 | 5 | 35 | 0 |
| 13.29 | 9 | 10 | 34 | 0 |
| 16.72 | 5 | 4 | 28 | 1 |
| 12.96 | 6 | 1 | 25 | 0 |
| 17.65 | 7 | 10 | 43 | 1 |
| 15.48 | 9 | 2 | 42 | 1 |
| 23.56 | 4 | 17 | 47 | 0 |
| 15.91 | 11 | 2 | 46 | 1 |
| 25.05 | 4 | 15 | 52 | 0 |
| 23.12 | 8 | 11 | 64 | 0 |
### Steps:
**a. Select the Competing Hypotheses:**
Determine whether the variance of hourly wages exceeds 35 (\(s^2\)).
- \(H_0: \sigma^2 \leq 35; \; H_A: \sigma^2 > 35\)
- \(H_0: \sigma^2 = 35; \; H_A: \sigma^2 \neq 35\)
- \(H_0: \sigma^2 \geq 35; \; H_A: \sigma^2 < 35\)
**b. Calculate the Test Statistic:**
Ensure intermediate calculations are rounded to at least 4 decimal places, and the final answer to 3 decimal places.
- Input Box: [Test Statistic] (This is where you input your calculated value)
**c. Find the p-value:**
Choose the correct range for the p-value.
- \(0.025 \leq \text{p-value} < 0.05\)
- \(0.01 \leq \text{p-value} < 0.025\)
- \(0.05 \leq \text{p-value} < 0.10\)
- \(\text{p-value} \geq 0.10\)
- \(\text{p-value} < 0.01\)
**d. Decision at 5% Significance Level:**
Determine if the variance of hourly wages exceeds \(35(s^2)\).
- Do not reject \(H_0\): We cannot conclude the variance of hourly wages exceeds \(35(s^2)\).
- Reject \(H_0\): We can conclude the variance of hourly wages exceeds \(35(s^2)\).
- Do not reject \(H_0\): We can conclude the variance of hourly wages exceeds \(35(s^2)\).
- Reject \(H_0\): We can conclude the variance of hourly wages exceeds \(35(s^2)\).
**Note:** Analyze the situation using the test statistic and p-value to make an informed decision on whether to reject the null hypothesis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F21d4eb06-eaa2-4705-83a6-21563ae4212f%2Fb8912691-590d-47ad-adde-81cbdf59b985%2Fbk0gj6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Hypothesis Testing on Variability of Hourly Wages**
An economist is researching the variability of hourly wages at a production plant. She collects data from 50 hourly wage earners. Use the accompanying Excel Data File for this exercise.
- [Link to Excel Data File](#)
### Steps:
**a. Select the Competing Hypotheses:**
Determine whether the variance of hourly wages exceeds 35 (\(s^2\)).
- \(H_0: \sigma^2 \leq 35; \; H_A: \sigma^2 > 35\)
- \(H_0: \sigma^2 = 35; \; H_A: \sigma^2 \neq 35\)
- \(H_0: \sigma^2 \geq 35; \; H_A: \sigma^2 < 35\)
**b. Calculate the Test Statistic:**
Ensure intermediate calculations are rounded to at least 4 decimal places, and the final answer to 3 decimal places.
- Input Box: [Test Statistic] (This is where you input your calculated value)
**c. Find the p-value:**
Choose the correct range for the p-value.
- \(0.025 \leq \text{p-value} < 0.05\)
- \(0.01 \leq \text{p-value} < 0.025\)
- \(0.05 \leq \text{p-value} < 0.10\)
- \(\text{p-value} \geq 0.10\)
- \(\text{p-value} < 0.01\)
**d. Decision at 5% Significance Level:**
Determine if the variance of hourly wages exceeds \(35(s^2)\).
- Do not reject \(H_0\): We cannot conclude the variance of hourly wages exceeds \(35(s^2)\).
- Reject \(H_0\): We can conclude the variance of hourly wages exceeds \(35(s^2)\).
- Do not reject \(H_0\): We can conclude the variance of hourly wages exceeds \(35(s^2)\).
- Reject \(H_0\): We can conclude the variance of hourly wages exceeds \(35(s^2)\).
**Note:** Analyze the situation using the test statistic and p-value to make an informed decision on whether to reject the null hypothesis.
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