You are testing the null hypothesis that there is no linear relationship between two variables, X and Y. From your sample of n = 18, you determine that b₁ = 4.3 and Sp, 1.4. a. What is the value of tSTAT? b. At the α = 0.05 level of significance, what are the critical values? c. Based on your answers to (a) and (b), what statistical decision should you make?

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You are testing the null hypothesis that there is no linear relationship between two variables, X and Y. From your sample of n = 18, you determine that \( b_1 = 4.3 \) and \( S_{b_1} = 1.4 \).

a. What is the value of \( t_{\text{STAT}} \)?

- \( t_{\text{STAT}} = 3.07 \) (Round to two decimal places as needed.)

b. At the \( \alpha = 0.05 \) level of significance, what are the critical values?
 
- The lower critical value is [blank].
- The upper critical value is [blank]. 
  (Round to four decimal places as needed.)

c. Based on your answers to (a) and (b), what statistical decision should you make?

d. Construct a 95% confidence interval estimate of the population slope, \( \beta_1 \).

### further information:

a. What are the hypotheses to test?

- Option A is selected:
  - \( H_0: \beta_1 = 0 \)
  - \( H_1: \beta_1 \neq 0 \)

Other options for hypotheses testing are:
- B. 
  - \( H_0: \beta_1 \leq 0 \)
  - \( H_1: \beta_1 > 0 \)
  
- C.
  - \( H_0: \beta_1 \geq 0 \)
  - \( H_1: \beta_1 < 0 \)
  
- D. 
  - \( H_0: \beta_1 \neq 0 \)
  - \( H_1: \beta_1 = 0 \)
Transcribed Image Text:You are testing the null hypothesis that there is no linear relationship between two variables, X and Y. From your sample of n = 18, you determine that \( b_1 = 4.3 \) and \( S_{b_1} = 1.4 \). a. What is the value of \( t_{\text{STAT}} \)? - \( t_{\text{STAT}} = 3.07 \) (Round to two decimal places as needed.) b. At the \( \alpha = 0.05 \) level of significance, what are the critical values? - The lower critical value is [blank]. - The upper critical value is [blank]. (Round to four decimal places as needed.) c. Based on your answers to (a) and (b), what statistical decision should you make? d. Construct a 95% confidence interval estimate of the population slope, \( \beta_1 \). ### further information: a. What are the hypotheses to test? - Option A is selected: - \( H_0: \beta_1 = 0 \) - \( H_1: \beta_1 \neq 0 \) Other options for hypotheses testing are: - B. - \( H_0: \beta_1 \leq 0 \) - \( H_1: \beta_1 > 0 \) - C. - \( H_0: \beta_1 \geq 0 \) - \( H_1: \beta_1 < 0 \) - D. - \( H_0: \beta_1 \neq 0 \) - \( H_1: \beta_1 = 0 \)
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“Since you have posted a question with multiple sub-parts, we will solve first three subparts for you. To get the remaining sub-parts solved, please repost the complete question and mention the sub-parts to be solved.”

Given that:

Sample size, n=18

Slope coefficient, b1=4.3

Standard error of slope coefficient, Sb1=1.4

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