Question

Data: Biologists have identified two subspecies of largemouth bass swimming in US waters, the Florida largemouth bass and the Northern largemouth bass. On two recent fishing trips you have recorded the weights of fish you have captured and released. Use this data to test the claim that the mean weight of the Florida bass is different from the mean weight of the Northern bass. Use α = .05 .

Florida bass weights (subscript F), in pounds:

5, 6, 5, 8, 12, 11, 10, 7, 16, 13

Northern bass weights (subscript N), in pounds:

5, 8, 3, 4, 7, 10, 12, 9, 6, 10

(Hint: If the populations are not independent, use subscript d = F - N. If the populations are independent, assume unequal variances.).

Question 1:Express the claim in symbolic form.

Group of answer choices

A) μ_F - μ_N ≠ 0

B) μ_F - μ_N ≥ 0

C) μ_F - μ_N ≤ 0

D) μ_d ≥ 0

E) μ_d = 0

F) μ_F - μ_N < 0

G) μ_d > 0

H) μ_d < 0

I) μ_F - μ_N = 0

J) μ_F - μ_N > 0

K) μ_d ≠ 0

L ) μ_d ≤ 0

Question 2) What is the alternative hypothesis, H₁?

Group of answer choices

A) μ_F - μ_N ≥ 0

B) μ_d ≠ 0

C) μ_d ≤ 0

D) μ_d = 0

E) μ_F - μ_N = 0

F) μ_d ≥ 0

G) μ_F - μ_N ≤ 0

H) μ_F - μ_N > 0

I) μ_F - μ_N < 0

J) μ_F - μ_N ≠ 0

K) μ_d < 0

L) μ_d > 0

3) Find the critical value(s). (Round to the nearest thousandth. If more than one value is found, enter the smallest critical value.)

4) Find the value of the test statistic. (Round to the nearest thousandth.)

5) What is the statistical conclusion?

Group of answer choices

A) Reject H₀

B) Fail to reject H₀

₆₎ State the conclusion in words.

Group of answer choices

A) There is not sufficient sample evidence to support the claim that the mean weight of the Florida bass is different from the mean weight of the Northern bass.

B) There is not sufficient evidence to warrant rejection of the claim that the mean weight of the Florida bass is different from the mean weight of the Northern bass.

C) There is sufficient evidence to warrant rejection of the claim that the mean weight of the Florida bass is different from the mean weight of the Northern bass.

D) The sample data support the claim that the mean weight of the Florida bass is different from the mean weight of the Northern bass.

Answer 1

Answer: Biologists have identified two subspecies of largemouth bass swimming in US waters, the Florida largemouth bass and the Northern largemouth bass. On two recent fishing trips you have recorded the weights of fish you have captured and released. Use this data to test the claim that the mean weight of the Florida bass is different from the mean weight of the Northern bass. Use α = .05 .

Solution:

1) Null hypothesis, Ho: μF - μN = 0

Alternative hypothesis, Ha: μF - μN ≠ 0

Florida bass weights (subscript F), in pounds:

5, 6, 5, 8, 12, 11, 10, 7, 16, 13

Mean, x̄F = Σx/n

Mean, x̄F = (5 + 6 +.......+16 + 13)/10

Mean, x̄F = 93/10

Mean, x̄F = 9.3

Std.D, SF = √((x​​​​​​i - x̄)2/n-1)

SF = √((x​​​​​​i​​​​​ - 9.3)2/10-1)

SF = √(124.1/9)

SF = 3.71

Northern bass weights (subscript N), in pounds:

5, 8, 3, 4, 7, 10, 12, 9, 6, 10

Mean, x̄N = (5 + 8 +.....+ 6 + 10)/10

Mean, x̄N = 74/10

Mean, x̄N = 7.4

Std.D, SN = √(xi - 7.4)2/10-1

SN = √76.4/9

SN = 2.91

3) the critical value:

6) there is not sufficient evidence to support the claim that the mean weight of the Florida bass is different from the mean weight of the Northern bass.

The option A. is correct answer.