Question

A comparison between species: Biologists comparing the gestation period of two newly discovered species of frog collected data from 13 frogs of species A and 22 frogs of species B. Species A exhibited an average gestation period of 13 days with a standard deviation of 3.4 days while species B had a gestation period of 17 days and a standard deviation of 2.6 days. The researchers want to know whether the average lengths of the gestational periods differ between the two species. Conduct a hypothesis test at a significance level of α=0.01.

a) The hypotheses for this test are:

• H₀: μ_A - μ_B = 0
  H_a: μ_A - μ_B ≠ 0
• H₀: μ_A - μ_B = 0
  H_a: μ_A - μ_B > 0
• H₀: μ_A - μ_B = 0
  H_a: μ_A - μ_B < 0
• H₀: μ_B = 13
  H_a: μ_B ≠ 13

b) What is the test statistic for this test?  (Report answer accurate to 2 decimal places.)

c.) What is the p-value for this test?   (Report answer accurate to 4 decimal places.)

d) The decision reached is

• Reject H₀ and accept H_a
• Fail to reject H₀

e) As such, the final conclusion is that

• There is significant evidence to suggest a difference between the lengths of the two species' gestational periods
• There is not significant evidence to suggest a difference between the lengths of the two species' gestational periods
• The lengths of the gestational periods are the same.
• There is significant evidence that suggests no difference in the lengths of the gestational periods.

Answer 1

The statistical software output for this problem is :

Option A is correct .

Test statistics = 3.65

P-value = 0.0015

Reject H₀

There is significant evidence to suggest a difference between the lengths of the two species' gestational periods