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Consider the following data for a dependent variable yand two independent variables,

x₁

and

x₂.

x1	x2	y
30	12	93
47	10	108
25	17	112
51	16	178
40	5	94
51	19	175
74	7	170
36	12	117
59	13	142
76	16	210

The estimated regression equation for these data is

Å· = −18.21 + 2.01x₁ +4.72x₂.

Here, SST = 15,134.9, SSR = 13,994.6,

s_b1 =0.2482,

and

s_b2 =0.9524.

(a)

Test for a significant relationship among

x₁,x₂, and y.

Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₁ >β₂
H_a: β₁ ≤β₂H₀:β₁ = β₂ = 0
H_a: One or more of the parameters is not equalto zero.     H₀:β₁ ≠ 0 and β₂ ≠ 0
H_a: One or more of the parameters is equal tozero.H₀: β₁ ≠ 0 andβ₂ = 0
H_a: β₁ = 0 andβ₂ ≠ 0H₀:β₁ < β₂
H_a: β₁ ≥β₂

Find the value of the test statistic. (Round your answer to twodecimal places.)

Find the p-value. (Round your answer to three decimalplaces.)

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence toconclude that there is a significant relationship among thevariables.Do not reject H₀. There isinsufficient evidence to conclude that there is a significantrelationship among the variables.     Donot reject H₀. There is sufficient evidence toconclude that there is a significant relationship among thevariables.Reject H₀. There is insufficientevidence to conclude that there is a significant relationship amongthe variables.

(b)

Is

β₁

significant? Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₁ = 0
H_a: β₁ ≠0H₀: β₁ < 0
H_a: β₁ ≥0     H₀:β₁ > 0
H_a: β₁ ≤0H₀: β₁ = 0
H_a: β₁ >0H₀: β₁ ≠ 0
H_a: β₁ = 0

Find the value of the test statistic. (Round your answer to twodecimal places.)

Find the p-value. (Round your answer to three decimalplaces.)

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence toconclude that β₁ is significant.RejectH₀. There is insufficient evidence to concludethat β₁ issignificant.     Do not rejectH₀. There is sufficient evidence to concludethat β₁ is significant.Do not rejectH₀. There is insufficient evidence to concludethat β₁ is significant.

(c)

Is

β₂

significant? Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₂ < 0
H_a: β₂ ≥0H₀: β₂ > 0
H_a: β₂ ≤0     H₀:β₂ ≠ 0
H_a: β₂ =0H₀: β₂ = 0
H_a: β₂ ≠0H₀: β₂ = 0
H_a: β₂ > 0

Find the value of the test statistic. (Round your answer to twodecimal places.)

Find the p-value. (Round your answer to three decimalplaces.)

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence toconclude that β₂ is significant.Do not rejectH₀. There is sufficient evidence to concludethat β₂ issignificant.     Do not rejectH₀. There is insufficient evidence to concludethat β₂ is significant.RejectH₀. There is insufficient evidence to concludethat β₂ is significant.