A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Connecticut and California. Due to recent trends in the childcare industry, the firm suspects that the that the mean annual income of childcare workers in the state of Connecticut is greater than the mean annual income of childcare workers in California. To see if this is true, the firm selected a random sample of 10 childcare workers from Connecticut and an independent random sample of 10 childcare workers from California and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars Connecticut 55657, 43863, 56330, 48932, 55059, 49205, 61868, 47883, 48196, 41987 California 43958, 47298, 46737, 45018, 54701, 39576, 54263, 36978, 49494, 48707 Send data to Excel Send data to calculator The population standard deviations for the annual incomes of childcare workers in Connecticut and in California are estimated as 6300 and 6100, respectively. It is also known that both populations are approximately normally distributed. At the 0.01 level of significance, is there sufficient evidence to support the claim that the mean annual income, H₁, of childcare workers in Connecticut is greater than the mean annual income, μ₂, of childcare workers in California? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. H:0 H₁:0 (b) Determine the type of test statistic to use. Explanation Check μ |x 4 a Р S ô 2 DO
A nationwide job recruiting firm wants to compare the annual incomes for childcare workers in Connecticut and California. Due to recent trends in the childcare industry, the firm suspects that the that the mean annual income of childcare workers in the state of Connecticut is greater than the mean annual income of childcare workers in California. To see if this is true, the firm selected a random sample of 10 childcare workers from Connecticut and an independent random sample of 10 childcare workers from California and asked them to report their mean annual income. The data obtained were as follows. Annual income in dollars Connecticut 55657, 43863, 56330, 48932, 55059, 49205, 61868, 47883, 48196, 41987 California 43958, 47298, 46737, 45018, 54701, 39576, 54263, 36978, 49494, 48707 Send data to Excel Send data to calculator The population standard deviations for the annual incomes of childcare workers in Connecticut and in California are estimated as 6300 and 6100, respectively. It is also known that both populations are approximately normally distributed. At the 0.01 level of significance, is there sufficient evidence to support the claim that the mean annual income, H₁, of childcare workers in Connecticut is greater than the mean annual income, μ₂, of childcare workers in California? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. H:0 H₁:0 (b) Determine the type of test statistic to use. Explanation Check μ |x 4 a Р S ô 2 DO
MATLAB: An Introduction with Applications
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Author:Amos Gilat
Publisher:Amos Gilat
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Transcribed Image Text:**Analysis of Childcare Workers’ Annual Incomes in Connecticut and California**
A nationwide job recruiting firm aims to compare the annual incomes for childcare workers in Connecticut and California. Due to industry trends, it's suspected that childcare workers in Connecticut may earn more on average than their counterparts in California. To verify this, the firm collected income data from random samples of 10 childcare workers from each state. Below is the data they obtained:
**Annual Income in Dollars**
- **Connecticut:** 55657, 43863, 56330, 48932, 55059, 49205, 61868, 47883, 48196, 41987
- **California:** 43958, 47298, 46737, 45018, 54701, 39576, 54263, 36978, 49494, 48707
The **population standard deviations** are estimated to be 6300 for Connecticut and 6100 for California, with both populations assumed to be **normally distributed**. Testing is carried out at a **0.01 level of significance** to determine if Connecticut's mean income (\( \mu_1 \)) is significantly greater than California's mean income (\( \mu_2 \)) through a **one-tailed test**.
**Hypothesis Testing:**
(a) **Null Hypothesis (\( H_0 \))**: \( \mu_1 = \mu_2 \)
**Alternative Hypothesis (\( H_1 \))**: \( \mu_1 > \mu_2 \)
(b) Determine the appropriate **test statistic** to compare the two means.
**Key considerations:**
- Ensure calculations are accurate to three decimal places.
- Consult necessary statistical formulas as needed.
This analysis aims to provide clarity on income disparities and contribute to informed policy-making or employment strategies in the childcare sector.
![### Hypothesis Testing Exercise
1. **Statement of Hypotheses:**
- **(a)** State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).
\[
H_0: \square
\]
\[
H_1: \square
\]
2. **Test Statistic:**
- **(b)** Determine the type of test statistic to use.
- **Options:** Drop-down list (Choose one)
3. **Calculate Test Statistic:**
- **(c)** Find the value of the test statistic. (Round to three or more decimal places.)
\[
\square
\]
4. **P-Value:**
- **(d)** Find the p-value. (Round to three or more decimal places.)
\[
\square
\]
5. **Conclusion:**
- **(e)** Can we support the claim that the mean annual income of childcare workers in Connecticut is greater than the mean annual income of childcare workers in California?
- **Options:** Yes / No
### Symbol Selection Panel
A panel on the right shows various statistical symbols and operators, including:
- Greek letters (\(\mu\), \(\sigma\), \(\rho\))
- Arithmetic symbols (\(x\), \(\overline{x}\), \(s\), \(\hat{p}\))
- Various hypothesis and comparison symbols.
To enter your calculations, select the appropriate symbols and operators from this panel.
---
This template guides you through conducting a hypothesis test on the difference in mean annual income between childcare workers in Connecticut and California. Follow each step carefully, and use the provided tools for accurate calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab310076-c445-4f02-aa72-05faca788dac%2F56f0133b-8e86-425b-9964-f4502ab01dbb%2Fiav9se_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing Exercise
1. **Statement of Hypotheses:**
- **(a)** State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).
\[
H_0: \square
\]
\[
H_1: \square
\]
2. **Test Statistic:**
- **(b)** Determine the type of test statistic to use.
- **Options:** Drop-down list (Choose one)
3. **Calculate Test Statistic:**
- **(c)** Find the value of the test statistic. (Round to three or more decimal places.)
\[
\square
\]
4. **P-Value:**
- **(d)** Find the p-value. (Round to three or more decimal places.)
\[
\square
\]
5. **Conclusion:**
- **(e)** Can we support the claim that the mean annual income of childcare workers in Connecticut is greater than the mean annual income of childcare workers in California?
- **Options:** Yes / No
### Symbol Selection Panel
A panel on the right shows various statistical symbols and operators, including:
- Greek letters (\(\mu\), \(\sigma\), \(\rho\))
- Arithmetic symbols (\(x\), \(\overline{x}\), \(s\), \(\hat{p}\))
- Various hypothesis and comparison symbols.
To enter your calculations, select the appropriate symbols and operators from this panel.
---
This template guides you through conducting a hypothesis test on the difference in mean annual income between childcare workers in Connecticut and California. Follow each step carefully, and use the provided tools for accurate calculations.
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