The summary statistics for a certain set of points are: =121.93, and b₁ = 2.91. n=25, s=3.43, Σ (x-x)² =1 Assume the conditions of the linear model hold. A 98% confidence interval for B, will be constructed. Part 1 of 4 How many degrees of freedom are there for the critical value? The degrees of freedom for the critical value are 23. Part: 1/4 Part 2 of 4 What is the critical value? Round the answer to three decimal places. 0. The critical value is

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The summary statistics for a certain set of points are:
n=25, s₂=3.43, Σ (x-x)² =121.93, and b₁ =2.91.
Assume the conditions of the linear model hold. A 98% confidence interval for B₁ will be constructed.
Part 1 of 4
How many degrees of freedom are there for the critical value?
The degrees of freedom for the critical value are 23.
Part: 1/4
Part 2 of 4
What is the critical value? Round the answer to three decimal places.
The critical value is
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Transcribed Image Text:ab Nock esc The summary statistics for a certain set of points are: n=25, s₂=3.43, Σ (x-x)² =121.93, and b₁ =2.91. Assume the conditions of the linear model hold. A 98% confidence interval for B₁ will be constructed. Part 1 of 4 How many degrees of freedom are there for the critical value? The degrees of freedom for the critical value are 23. Part: 1/4 Part 2 of 4 What is the critical value? Round the answer to three decimal places. The critical value is Skip Part F1 1 option - Z Check 8 2 F2 W S # 3 X H command 20 F3 E $ 4 C DOO DOD F4 R F olo LO % 5 F5 V T G <CO 6 X F6 Y B 7 H S F7 © 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use Priva с N * 8 F8 9 Save For Later M (TANERINGKA H P
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13.1
1
Question 3 of 15 (1 point) Question Attempt: 1 of Unlimited
For the 50 U.S. states, the sample correlation coefficient relating the 1980 per capita income and the 1999 per capita income is approximately 0.32 (source:
U.S. Bureau of Economic Analysis, Survey of Current Business, May 2000). Based on this information, test for a significant linear relationship between the
variables 1980 per capita income and 1999 per capita income by doing a hypothesis test regarding the population correlation coefficient p. (Assume that the two
variables have a bivariate normal distribution.) Use the 0.05 level of significance, and perform a two-tailed test. Then complete the parts below.
(If necessary, consult a list of formulas.)
(a) State the null hypothesis Ho and the alternative hypothesis H₁.
H₁ : p=0
H₁ : p = 0
(b) Determine the type of test statistic to use.
(c) Find the value of the test statistic. (Round to three or more decimal places.)
2.340
Z
(d) Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.)
and
(e) Based on the data, can we conclude (using the 0.05 level) that there is a significant linear
relationship between 1980 per capita income and 1999 per capita income for U.S. states?
OYes O No
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Transcribed Image Text:esc 13.1 1 Question 3 of 15 (1 point) Question Attempt: 1 of Unlimited For the 50 U.S. states, the sample correlation coefficient relating the 1980 per capita income and the 1999 per capita income is approximately 0.32 (source: U.S. Bureau of Economic Analysis, Survey of Current Business, May 2000). Based on this information, test for a significant linear relationship between the variables 1980 per capita income and 1999 per capita income by doing a hypothesis test regarding the population correlation coefficient p. (Assume that the two variables have a bivariate normal distribution.) Use the 0.05 level of significance, and perform a two-tailed test. Then complete the parts below. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. H₁ : p=0 H₁ : p = 0 (b) Determine the type of test statistic to use. (c) Find the value of the test statistic. (Round to three or more decimal places.) 2.340 Z (d) Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.) and (e) Based on the data, can we conclude (using the 0.05 level) that there is a significant linear relationship between 1980 per capita income and 1999 per capita income for U.S. states? OYes O No Check Z 2 F2 W S X H option command # 3 20 F3 E C $ 4 DOO 000 F4 R F % 5 V .- F5 T G <CO 6 MacBook Air B F6 Y & 7 H F7 с N 8 J F8 M В XI 010 0>0 X 020 0#0 0<0 ( 9 K Р 0=0 0≤0 Ś © 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessi F9 H ? Save For Later L H O L F10 P command Submit Assignm Ô F11 De t { + 11 ? option
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