Question

Problem 2" (20%) Biologists have theorized that male monarch butterflies have, on average, a larger thorax (body) than do females. Sample of butterflies were collected and weights were collected yielded the following table of summary data. Male (sample 1) 17 Female (sample 2) 28 75.7 8.4 Mean 72.5 St. Dev Stand. Error 1.42 2.04 The 95% confidence interval of the difference of means is computed as (-1.8, 8.21). Can we reject the following hypothesis:Do not compute iust-Yes No and reasons) Ho: there is no difference of weight of thorax between male and female butterflies. Vs. Ha: Their means are different. (Using significance level a-0.05?)

Answer 1

Null and alternative hypotheses are,

H₀: There is no difference of weight of thorax between male and female butterflies.

H_a : Their mean are different.

Null and alternative hypotheses in symbol,

$H_0: \mu_M -\mu_F = 0$

$H_a: \mu_M -\mu_F \neq 0$

The 95% confidence interval ofthe difference of means is computed as (-1.8, 8.21)

Since , zero (0) contains in above 95% confidence interval we do not reject (or fail to reject ) the null hypothesis.

Answer: No, because interval contains zero(0).