You may need to use the appropriate technology to answer this question. Consider the data. X₁269 13 20 Y₁ 6 20 11 27 21 (a) What is the value of the standard error of the estimate? (Round your answer to three decimal places.) (b) Test for a significant relationship by using the t test. Use a = 0.05. State the null and alternative hypotheses. Ho: ₁0 Ha: ₁0 Ho: P₁0 H₂: B₂ O Ho: B₂ 20 O Ho: Po o Hồ ly=0 ○ Ho: Po=0 Ha: Po *0 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value= State your conclusion. O Do not reject Ho. We cannot conclude that the relationship between x and y is significant. O Reject Ho. We cannot conclude that the relationship between x and y is significant. O Do not reject Ho- We conclude that the relationship between x and y is significant. O Reject Ho. We conclude that the relationship between x and y is significant. (c) Use the F test to test for a significant relationship. Use a = 0.05. State the null and alternative hypotheses. Ho: Boo Hai Boo ○ Ho: B₂ = 0 H₂: B₂ 0 O Ho: Po o H₂ P=0 O Ho: B₂0 H₂: ₁0 O Ho: B₂ 20 Hỷ Đo Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value=
You may need to use the appropriate technology to answer this question. Consider the data. X₁269 13 20 Y₁ 6 20 11 27 21 (a) What is the value of the standard error of the estimate? (Round your answer to three decimal places.) (b) Test for a significant relationship by using the t test. Use a = 0.05. State the null and alternative hypotheses. Ho: ₁0 Ha: ₁0 Ho: P₁0 H₂: B₂ O Ho: B₂ 20 O Ho: Po o Hồ ly=0 ○ Ho: Po=0 Ha: Po *0 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value= State your conclusion. O Do not reject Ho. We cannot conclude that the relationship between x and y is significant. O Reject Ho. We cannot conclude that the relationship between x and y is significant. O Do not reject Ho- We conclude that the relationship between x and y is significant. O Reject Ho. We conclude that the relationship between x and y is significant. (c) Use the F test to test for a significant relationship. Use a = 0.05. State the null and alternative hypotheses. Ho: Boo Hai Boo ○ Ho: B₂ = 0 H₂: B₂ 0 O Ho: Po o H₂ P=0 O Ho: B₂0 H₂: ₁0 O Ho: B₂ 20 Hỷ Đo Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value=
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 76E
Related questions
Question
![### Consider the Data
\[
\begin{array}{c|ccccc}
x_i & 7 & 6 & 9 & 13 & 20 \\
y_i & 6 & 20 & 11 & 27 & 21 \\
\end{array}
\]
**(a) What is the value of the standard error of the estimate? (Round your answer to three decimal places.)**
**Answer:**
\[ \text{Standard Error} = \underline{\hspace{4cm}} \]
**(b) Test for a significant relationship by using the t test. Use \(\alpha = 0.05\).**
1. **State the null and alternative hypotheses.**
- \[
\begin{array}{c}
\text{Null Hypothesis, } H_0: \beta_1 = 0 \\
\text{Alternative Hypothesis, } H_1: \beta_1 \neq 0 \\
\end{array}
\]
2. **Find the value of the test statistic. (Round your answer to three decimal places.)**
**Test Statistic: ** \( \underline{\hspace{4cm}} \)
3. **Find the p-value. (Round your answer to four decimal places.)**
**p-value: ** \( \underline{\hspace{4cm}} \)
4. **State your conclusion.**
\(\circ\) Do not reject \( H_0 \). We cannot conclude that the relationship between \( x \) and \( y \) is significant.
\(\circ\) Reject \( H_0 \). We conclude that the relationship between \( x \) and \( y \) is significant.
**(c) Use the t test to test for a significant relationship. Use \(\alpha = 0.05\).**
1. **State the null and alternative hypotheses.**
- \[
\begin{array}{c}
\text{Null Hypothesis, } H_0: \beta_1 = 0 \\
\text{Alternative Hypothesis, } H_1: \beta_1 \neq 0 \\
\end{array}
\]
2. **Find the value of the test statistic. (Round your answer to two decimal places.)**
**Test Statistic: ** \( \underline{\h](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F928f3826-faea-4936-b5b6-4aab28469498%2Fc0fd7f0b-788d-46dc-b903-3630e060e377%2F7xqsuh8_processed.png&w=3840&q=75)
Transcribed Image Text:### Consider the Data
\[
\begin{array}{c|ccccc}
x_i & 7 & 6 & 9 & 13 & 20 \\
y_i & 6 & 20 & 11 & 27 & 21 \\
\end{array}
\]
**(a) What is the value of the standard error of the estimate? (Round your answer to three decimal places.)**
**Answer:**
\[ \text{Standard Error} = \underline{\hspace{4cm}} \]
**(b) Test for a significant relationship by using the t test. Use \(\alpha = 0.05\).**
1. **State the null and alternative hypotheses.**
- \[
\begin{array}{c}
\text{Null Hypothesis, } H_0: \beta_1 = 0 \\
\text{Alternative Hypothesis, } H_1: \beta_1 \neq 0 \\
\end{array}
\]
2. **Find the value of the test statistic. (Round your answer to three decimal places.)**
**Test Statistic: ** \( \underline{\hspace{4cm}} \)
3. **Find the p-value. (Round your answer to four decimal places.)**
**p-value: ** \( \underline{\hspace{4cm}} \)
4. **State your conclusion.**
\(\circ\) Do not reject \( H_0 \). We cannot conclude that the relationship between \( x \) and \( y \) is significant.
\(\circ\) Reject \( H_0 \). We conclude that the relationship between \( x \) and \( y \) is significant.
**(c) Use the t test to test for a significant relationship. Use \(\alpha = 0.05\).**
1. **State the null and alternative hypotheses.**
- \[
\begin{array}{c}
\text{Null Hypothesis, } H_0: \beta_1 = 0 \\
\text{Alternative Hypothesis, } H_1: \beta_1 \neq 0 \\
\end{array}
\]
2. **Find the value of the test statistic. (Round your answer to two decimal places.)**
**Test Statistic: ** \( \underline{\h
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