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The population standard deviation for the annual incomes of childcare workers in Texas and in Indiana are estimated as 6200 and 6500, 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 Texas is less than the mean annual income, μ₂, of childcare workers in Indiana? 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 O Р S P HO H₁:0 00 (b) Determine the type of test statistic to use. (Choose one) ▼ 0=0 OSO 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 00 >O ? (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we support the claim that the mean annual income of childcare workers in Texas is less than the mean annual incom of childcare workers in Indiana? Yes No + 7 O

The population standard deviation for the annual incomes of childcare workers in Texas and in Indiana are estimated as 6200 and 6500, 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 Texas is less than the mean annual income, μ₂, of childcare workers in Indiana? 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 O Р S P HO H₁:0 00 (b) Determine the type of test statistic to use. (Choose one) ▼ 0=0 OSO 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 00 >O ? (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we support the claim that the mean annual income of childcare workers in Texas is less than the mean annual incom of childcare workers in Indiana? Yes No + 7 O

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Comparison of Annual Incomes of Childcare Workers in Texas and Indiana #### Introduction A nationwide job recruiting firm aims to compare the annual incomes of childcare workers in Texas and Indiana. Due to recent trends in the childcare industry, the firm suspects that the mean annual income of childcare workers in Texas is less than the mean annual income of childcare workers in Indiana. To validate this hypothesis, the firm sampled 25 childcare workers from Texas and 25 from Indiana, requesting them to report their mean annual income. The data obtained are as follows: #### Data **Annual Income in Dollars:** - **Texas:** 30111, 35543, 34245, 42733, 40077, 22500, 35332, 32416, 38243, 7548, 34262, 31505, 37073, 31673, 33941, 32640, 27860, 29796, 32562, 36992, 35943, 40878, 84072, 29520, 32661 - **Indiana:** 42600, 30305, 33346, 42456, 34420, 30741, 38497, 38950, 40314, 41701, 43402, 33090, 39851, 36107, 45694, 36270, 39027, 39300, 43787, 44748, 40842 #### Population Standard Deviation The population standard deviations for the annual incomes of childcare workers in Texas and Indiana are estimated as $6200 and $6500, respectively. It is also known that both populations are approximately normally distributed. #### Hypothesis Testing at 0.01 Level of Significance To determine if there is sufficient evidence to support the claim that the mean annual income (\( \mu_1 \)) of childcare workers in Texas is less than the mean annual income (\( \mu_2 \)) of childcare workers in Indiana, we perform a one-tailed test. The following steps outline the hypothesis testing process: 1. **State the Null Hypothesis \( H_0 \) and the Alternative Hypothesis \( H_1 \):** \[ H_0: \mu_1 \geq \mu_2 \] \[ H_1: \
Transcribed Image Text:### Comparison of Annual Incomes of Childcare Workers in Texas and Indiana #### Introduction A nationwide job recruiting firm aims to compare the annual incomes of childcare workers in Texas and Indiana. Due to recent trends in the childcare industry, the firm suspects that the mean annual income of childcare workers in Texas is less than the mean annual income of childcare workers in Indiana. To validate this hypothesis, the firm sampled 25 childcare workers from Texas and 25 from Indiana, requesting them to report their mean annual income. The data obtained are as follows: #### Data **Annual Income in Dollars:** - **Texas:** 30111, 35543, 34245, 42733, 40077, 22500, 35332, 32416, 38243, 7548, 34262, 31505, 37073, 31673, 33941, 32640, 27860, 29796, 32562, 36992, 35943, 40878, 84072, 29520, 32661 - **Indiana:** 42600, 30305, 33346, 42456, 34420, 30741, 38497, 38950, 40314, 41701, 43402, 33090, 39851, 36107, 45694, 36270, 39027, 39300, 43787, 44748, 40842 #### Population Standard Deviation The population standard deviations for the annual incomes of childcare workers in Texas and Indiana are estimated as $6200 and $6500, respectively. It is also known that both populations are approximately normally distributed. #### Hypothesis Testing at 0.01 Level of Significance To determine if there is sufficient evidence to support the claim that the mean annual income (\( \mu_1 \)) of childcare workers in Texas is less than the mean annual income (\( \mu_2 \)) of childcare workers in Indiana, we perform a one-tailed test. The following steps outline the hypothesis testing process: 1. **State the Null Hypothesis \( H_0 \) and the Alternative Hypothesis \( H_1 \):** \[ H_0: \mu_1 \geq \mu_2 \] \[ H_1: \
### Hypothesis Testing for Childcare Workers' Salaries In this exercise, we are given the task of determining whether the mean annual income of childcare workers in Texas is less than that in Indiana. The population standard deviation for the annual incomes of childcare workers in both states is provided, and both populations are assumed to be approximately normally distributed. We will use a significance level of 0.01 and conduct a one-tailed test. #### Problem Statement The annual incomes of childcare workers in Texas and Indiana are estimated to be 6200 and 6500, respectively. At the 0.01 level of significance, is there sufficient evidence to support the claim that the mean annual income \( \mu_1 \) of childcare workers in Texas is less than the mean annual income \( \mu_2 \) of childcare workers in Indiana? #### Procedure Carry out the following steps and provide intermediate computations to at least three decimal places: 1. **State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).** \( H_0 : \mu_1 = \mu_2 \) \( H_1 : \mu_1 < \mu_2 \) 2. **Determine the type of test statistic to use.** (Select the appropriate statistical test from the available options.) 3. **Calculate the value of the test statistic.** (Provide the value rounded to three or more decimal places.) 4. **Find the p-value.** (Provide the p-value rounded to three or more decimal places.) 5. **Decision on the hypothesis.** Based on the p-value, determine whether there is sufficient evidence to support the claim that the mean annual income of childcare workers in Texas is less than that in Indiana: Can we support the claim that the mean annual income of childcare workers in Texas is less than the mean annual income of childcare workers in Indiana? - Yes - No #### Explanation of Diagram/Graph (if any) The image does not present any graphs or diagrams to describe. It consists solely of text fields and dropdown menus for entering information related to hypothesis testing. --- This exercise guides you through using hypothesis tests to compare two population means and interpret the results to understand differences in income between childcare workers in two states.
Transcribed Image Text:### Hypothesis Testing for Childcare Workers' Salaries In this exercise, we are given the task of determining whether the mean annual income of childcare workers in Texas is less than that in Indiana. The population standard deviation for the annual incomes of childcare workers in both states is provided, and both populations are assumed to be approximately normally distributed. We will use a significance level of 0.01 and conduct a one-tailed test. #### Problem Statement The annual incomes of childcare workers in Texas and Indiana are estimated to be 6200 and 6500, respectively. At the 0.01 level of significance, is there sufficient evidence to support the claim that the mean annual income \( \mu_1 \) of childcare workers in Texas is less than the mean annual income \( \mu_2 \) of childcare workers in Indiana? #### Procedure Carry out the following steps and provide intermediate computations to at least three decimal places: 1. **State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).** \( H_0 : \mu_1 = \mu_2 \) \( H_1 : \mu_1 < \mu_2 \) 2. **Determine the type of test statistic to use.** (Select the appropriate statistical test from the available options.) 3. **Calculate the value of the test statistic.** (Provide the value rounded to three or more decimal places.) 4. **Find the p-value.** (Provide the p-value rounded to three or more decimal places.) 5. **Decision on the hypothesis.** Based on the p-value, determine whether there is sufficient evidence to support the claim that the mean annual income of childcare workers in Texas is less than that in Indiana: Can we support the claim that the mean annual income of childcare workers in Texas is less than the mean annual income of childcare workers in Indiana? - Yes - No #### Explanation of Diagram/Graph (if any) The image does not present any graphs or diagrams to describe. It consists solely of text fields and dropdown menus for entering information related to hypothesis testing. --- This exercise guides you through using hypothesis tests to compare two population means and interpret the results to understand differences in income between childcare workers in two states.
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