Question

Consider the following regression results based on 40 observations. [You may find it useful to reference the t table.] Standard p- Coefficients Error t Stat value Intercept 40.4543 12.6945 3.187 0.003 x1 0.9157 0.9382 0.976 0.336 a. Specify the hypotheses to determine if the slope differs from minus one. H0: ?1 ? -1; HA: ?1 > -1 H0: ?1 ? -1; HA: ?1 < -1 H0: ?1 = -1; HA: ?1 ? -1 b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) Test statistic b-2. Find the p-value. 0.02 ? p-value < 0.05 0.01 ? p-value < 0.02 p-value < 0.01 p-value ? 0.10 0.05 ? p-value < 0.10 c. At the 2% significance level, can we conclude the slope differs from minus one? Yes, since the p-value is less than the significance level. No, since the p-value is more than the significance level. Yes, since the p-value is more than the significance level. No, since the p-value is less than the significance level.

          Consider the following regression results based on 40 observations. [You may find it useful to reference the t table.]

Standard p-
Coefficients Error t Stat value
Intercept 40.4543 12.6945 3.187 0.003
x1 0.9157 0.9382 0.976 0.336

a. Specify the hypotheses to determine if the slope differs from minus one.
H0: ?1 ? -1; HA: ?1 > -1
H0: ?1 ? -1; HA: ?1 < -1
H0: ?1 = -1; HA: ?1 ? -1

b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)
Test statistic

b-2. Find the p-value.
0.02 ? p-value < 0.05
0.01 ? p-value < 0.02
p-value < 0.01
p-value ? 0.10
0.05 ? p-value < 0.10

c. At the 2% significance level, can we conclude the slope differs from minus one?
Yes, since the p-value is less than the significance level.
No, since the p-value is more than the significance level.
Yes, since the p-value is more than the significance level.
No, since the p-value is less than the significance level.

Show more…

Consider the following regression results based on 40 observations. [You may find it useful to reference the t table.]

Standard p-
Coefficients Error t Stat value
Intercept 40.4543 12.6945 3.187 0.003
x1 0.9157 0.9382 0.976 0.336

a. Specify the hypotheses to determine if the slope differs from minus one.
H0: ?1 ? -1; HA: ?1 > -1
H0: ?1 ? -1; HA: ?1 < -1
H0: ?1 = -1; HA: ?1 ? -1

b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)
Test statistic

b-2. Find the p-value.
0.02 ? p-value < 0.05
0.01 ? p-value < 0.02
p-value < 0.01
p-value ? 0.10
0.05 ? p-value < 0.10

c. At the 2% significance level, can we conclude the slope differs from minus one?
Yes, since the p-value is less than the significance level.
No, since the p-value is more than the significance level.
Yes, since the p-value is more than the significance level.
No, since the p-value is less than the significance level.

Added by Teresa T.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert David Nguyen

07/31/2022

Step 1

The hypotheses to determine if the slope differs from minus one would be: Ho: β1 = -1 (Null hypothesis: The slope is equal to -1) HA: β1 ≠ -1 (Alternative hypothesis: The slope is not equal to -1) Show more…

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Consider the following regression results based on 40 observations. [You may find it useful to reference the t table.] Standard p- Coefficients Error t Stat value Intercept 40.4543 12.6945 3.187 0.003 x1 0.9157 0.9382 0.976 0.336 a. Specify the hypotheses to determine if the slope differs from minus one. H0: ̢1 ≤ -1; HA: ̢1 > -1 H0: ̢1 ≥ -1; HA: ̢1 < -1 H0: ̢1 = -1; HA: ̢1 ≠ -1 b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) Test statistic b-2. Find the p-value. 0.02 ≤ p-value < 0.05 0.01 ≤ p-value < 0.02 p-value < 0.01 p-value ≥ 0.10 0.05 ≤ p-value < 0.10 c. At the 2% significance level, can we conclude the slope differs from minus one? Yes, since the p-value is less than the significance level. No, since the p-value is more than the significance level. Yes, since the p-value is more than the significance level. No, since the p-value is less than the significance level.

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Transcript

00:01 Hi, i'm david and i'm here to have you answering your question.

00:03 In the question here we are given the output on the data analysis.

00:08 And here in the question a, we need to specify the known and alternative hypothesis to determine if the slope differs from the minus 1.

00:17 It means that we have the known hypothesis, then the beta 1 equal to the minus 1 versus the alternative hypothesis that the beta 1 will not equal to the minus 1.

00:30 Minus 1.

00:31 Therefore the answer for this question here, it will be the third option.

00:38 And now for the question for the question b, we need to find the value of the test statistics.

00:45 The test statistic denoted by the t, the formula will be the p0 minus the p1 over the standard error.

00:53 Now we have the p0 in the table we have equal to the coefficient equals to 9157 we minus the p1 equal to the minus 1 there and then we will divide by the standard error it will equal to the 0 .9 382 and if we compute we will have the 1 .9 157 dividing by 0193 82 it will equal to the 2 .0402 i will write this one into the three decimal places and then for this one will be the p1 and here we have the p2 i need to find the p value here the p value it will equal to the probability of the t with the n minus 1 degree freedom and it will be for this one will be the two tell test it will be two times that greater than the test statistics so means that we 2 times the probability of the t here will have the n it will equal to the 40 observations here n minus 2 sorry and then n minus 2 will be the 40 minus 2 will be the 38 that greater than the 2 bonus 42 now to find the b value i need to become the t table let me copy the table and i will put the table down here now from the table to focus on the 38 degree freedom.

02:38 Here we don't have the 30m degree freedom.

02:40 We have only between the 30 and the 40.

02:43 So i will consider only both of them here...

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