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Consider the data.
x_{i} |
2 | 6 | 9 | 13 | 20 |
---|---|---|---|---|---|
y_{i} |
5 | 19 | 8 | 28 | 23 |
(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.
a) H_{0}: β_{0} = 0
H_{a}: β_{0} ≠ 0
b) H_{0}: β_{1} = 0
H_{a}: β_{1} ≠
0
c) H_{0}: β_{1} ≥ 0
H_{a}: β_{1} < 0
d) H_{0}: β_{0} ≠ 0
H_{a}: β_{0} = 0
e) H_{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.
a) Do not reject H_{0}. We conclude that the relationship between x and y is significant.
b) Do not reject H_{0}. We cannot conclude that the relationship between x and y is significant.
c) Reject H_{0}. We cannot conclude that the relationship between x and y is significant.
d) 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.
a)H_{0}: β_{0} = 0
H_{a}: β_{0} ≠ 0
b)H_{0}: β_{1} ≠ 0
H_{a}: β_{1} =
0
c) H_{0}: β_{1} ≥ 0
H_{a}: β_{1} < 0
d) H_{0}: β_{1} = 0
H_{a}: β_{1} ≠ 0
e) H_{0}: β_{0} ≠ 0
H_{a}: β_{0} = 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?
a) Reject H_{0}. We cannot conclude that the relationship between x and y is significant.
b) Do not reject H_{0}. We cannot conclude that the relationship between x and y is significant.
c) Do not reject H_{0}. We conclude that the relationship between x and y is significant.
d) Reject H_{0}. We conclude that the relationship between x and y is significant.
applying regression on above data from excel: data: data analysis:
a)
std error σ = | =se =√s^{2}= | 8.066 |
b)
b) H_{0}: β_{1} = 0
H_{a}: β_{1} ≠ 0
value of the test statistic= | (bo-β_{1})/se(β_{1})= | = | 1.709 |
p value: | = | 0.1860 |
b) Do not reject H_{0}. We cannot conclude that the relationship between x and y is significant.
c)
d) H_{0}: β_{1} = 0
H_{a}: β_{1} ≠ 0
value of the test statistic F =2.92
p-value =0.186
b) Do not reject H_{0}. We cannot conclude that the relationship between x and y is significant.
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