Question

Consider the data. [ egin{array}{|c|c|c|c|c|c|} hline x_{(i)} & 2 & 6 & 9 & 13 & 20 \ y_{(i)} & 7 & 20 & 11 & 26 & 24 \ hline end{array} ] (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 $alpha = 0.05$. State the null and alternative hypotheses. $H_{0}: eta_{0} eq 0$ $H_{a}: eta_{0} = 0$ $H_{0}: eta_{1} = 0$ $H_{a}: eta_{1} eq 0$ $H_{0}: eta_{1} eq 0$ $H_{a}: eta_{1} = 0$ $H_{0}: eta_{1} geq 0$ $H_{a}: eta_{1} < 0$ $H_{0}: eta_{0} = 0$ $H_{a}: eta_{0} eq 0$ 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. Do not reject $H_{0}$. We cannot conclude that the relationship between $x$ and $y$ is significant. Do not reject $H_{0}$. We conclude that the relationship between $x$ and $y$ is significant. Reject $H_{0}$. We cannot conclude that the relationship between $x$ and $y$ is significant. ◻ Reject $H_{0}$. We conclude that the relationship between $x$ and $y$ is significant. (c) Use the F test to test for a significant relationship. Use $alpha = 0.05$. State the null and alternative hypotheses. $H_{0}: eta_{1} = 0$ $H_{a}: eta_{1} eq 0$ $H_{0}: eta_{1} geq 0$ $H_{a}: eta_{1} < 0$ $H_{0}: eta_{0} eq 0$ $H_{a}: eta_{0} = 0$ $H_{0}: eta_{1} eq 0$ $H_{a}: eta_{1} = 0$ $H_{0}: eta_{0} = 0$ $H_{a}: eta_{0} eq 0$ 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 = What is your conclusion? Reject $H_{0}$. We cannot conclude that the relationship between $x$ and $y$ is significant. Do not reject $H_{0}$. We conclude that the relationship between $x$ and $y$ is significant. Reject $H_{0}$. We conclude that the relationship between $x$ and $y$ is significant. Do not reject $H_{0}$. We cannot conclude that the relationship between $x$ and $y$ is significant.

          Consider the data.
[
egin{array}{|c|c|c|c|c|c|}
hline
x_{(i)} & 2 & 6 & 9 & 13 & 20 \
y_{(i)} & 7 & 20 & 11 & 26 & 24 \
hline
end{array}
]
(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 $alpha = 0.05$.
State the null and alternative hypotheses.
$H_{0}: eta_{0} 
eq 0$
$H_{a}: eta_{0} = 0$
$H_{0}: eta_{1} = 0$
$H_{a}: eta_{1} 
eq 0$
$H_{0}: eta_{1} 
eq 0$
$H_{a}: eta_{1} = 0$
$H_{0}: eta_{1} geq 0$
$H_{a}: eta_{1} < 0$
$H_{0}: eta_{0} = 0$
$H_{a}: eta_{0} 
eq 0$
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.
Do not reject $H_{0}$. We cannot conclude that the relationship between $x$ and $y$ is significant.
Do not reject $H_{0}$. We conclude that the relationship between $x$ and $y$ is significant.
Reject $H_{0}$. We cannot conclude that the relationship between $x$ and $y$ is significant.
◻ Reject $H_{0}$. We conclude that the relationship between $x$ and $y$ is significant.
(c) Use the F test to test for a significant relationship. Use $alpha = 0.05$.
State the null and alternative hypotheses.
$H_{0}: eta_{1} = 0$
$H_{a}: eta_{1} 
eq 0$
$H_{0}: eta_{1} geq 0$
$H_{a}: eta_{1} < 0$
$H_{0}: eta_{0} 
eq 0$
$H_{a}: eta_{0} = 0$
$H_{0}: eta_{1} 
eq 0$
$H_{a}: eta_{1} = 0$
$H_{0}: eta_{0} = 0$
$H_{a}: eta_{0} 
eq 0$
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 =
What is your conclusion?
Reject $H_{0}$. We cannot conclude that the relationship between $x$ and $y$ is significant.
Do not reject $H_{0}$. We conclude that the relationship between $x$ and $y$ is significant.
Reject $H_{0}$. We conclude that the relationship between $x$ and $y$ is significant.
Do not reject $H_{0}$. We cannot conclude that the relationship between $x$ and $y$ is significant.

consider the data beginarraycccccc hline xi 2 6 9 13 20 yi 7 20 11 26 24 hline endarray a what is the value of the standard error of the estimate round your answer to three decimal places 73537

Added by Nicholas R.

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