Question

Toxaphene is an insecticide that has been identified as a pollutant in the Great Lakes ecosystem. To investigate the effect of toxaphene exposure on animals, groups of rats were given toxaphene in their diet. A study reports weight gains (in grams) for rats given a low dose (4 ppm) and for control rats whose diet did not include the insecticide. The sample standard deviation for 20 female control rats was 32 g and for 22 female low-dose rats was 58 g. Does this data suggest that there is more variability in low-dose weight gains than in control weight gains? Assuming normality, carry out a test of hypotheses at significance level 0.05.

State the relevant hypotheses. (Use σ₁ for low-dose treatment and σ₂ for control condition.)

H₀: σ₁² = σ₂²
H_a: σ₁² < σ₂²H₀: σ₁² = σ₂²
H_a: σ₁² > σ₂²     H₀: σ₁² = σ₂²
H_a: σ₁² ≠ σ₂²H₀: σ₁² = σ₂²
H_a: σ₁² ≥ σ₂²

Calculate the test statistic. (Round your answer to two decimal places.)
f =

What can be said about the P-value for the test?

P-value > 0.100

0.050 < P-value < 0.100    

0.010 < P-value < 0.050

0.001 < P-value < 0.010

P-value < 0.001

State the conclusion in the problem context.

Fail to reject H₀. The data suggests that there is more variability in the low-dose weight gains than in control weight gains.

Fail to reject H₀. The data does not suggest that there is more variability in the low-dose weight gains than in control weight gains.

Reject H₀. The data suggests that there is more variability in the low-dose weight gains than in control weight gains. Reject H₀.

The data does not suggest that there is more variability in the low-dose weight gains than in control weight gains.

Answer 1

State the relevant hypotheses. (Use σ₁ for low-dose treatment and σ₂ for control condition.)

The correct option is as follow:

H_a: σ₁² < σ₂²   H₀: σ₁² = σ₂²

Calculate the test statistic. (Round your answer to two decimal places.)

$F=\frac{s^{2}_{1}}{s^{2}_{1}}=\frac{58^2}{32^2}=\frac{3364}{1024}={\color{Red} 3.29}$

What can be said about the P-value for the test?

Degrees of freedom for numerator = 22 - 1 = 21

Degrees of freedom for denominator = 20 - 1 = 19

So p-value using excel is as

p-value = "=FDIST(3.29,21,19)" = 0.0058

Which is lies between 0.001 and 0.01

So correct choice is as "0.001 < P-value < 0.010"

State the conclusion in the problem context.

Decision rule:

1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here upper bound of the p value = 0.01 <  0.05 so we used first rule.

That is we reject null hypothesis

So correct choice is as

Reject H₀. The data suggests that there is more variability in the low-dose weight gains than in control weight gains. Reject H₀.