Consider the data.
x_{i} |
2 | 6 | 9 | 13 | 20 |
---|---|---|---|---|---|
y_{i} |
7 | 18 | 10 | 26 | 25 |
(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 α = 0.05.
State the null and alternative hypotheses.
H_{0}: β_{0} = 0
H_{a}: β_{0} ≠
0H_{0}: β_{1} ≥ 0
H_{a}: β_{1} <
0 H_{0}:
β_{1} ≠ 0
H_{a}: β_{1} =
0H_{0}: β_{0} ≠ 0
H_{a}: β_{0} =
0H_{0}: β_{1} = 0
H_{a}: β_{1} ≠ 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.
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. 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.
(c)
Use the F test to test for a significant relationship. Use α = 0.05.
State the null and alternative hypotheses.
H_{0}: β_{1} ≥ 0
H_{a}: β_{1} <
0H_{0}: β_{1} ≠ 0
H_{a}: β_{1} =
0 H_{0}:
β_{0} ≠ 0
H_{a}: β_{0} =
0H_{0}: β_{0} = 0
H_{a}: β_{0} ≠
0H_{0}: β_{1} = 0
H_{a}: β_{1} ≠ 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. Do not 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.
For the given data using Regression in Excel we get output as
So from the above output
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