Question

An examination in biology has been taken by biology majors and also by some students from other majors. It is widely believed that the scores for both groups are normally distributed. A random sample of 24 examinations completed by biology majors and an independent random sample of 23 examinations completed by students from other majors are selected. Among sampled students, the biology majors scored a mean of 532.8 points with a variance of 9101.16, and the students from other majors scored a mean of 509.6 points with a variance of 16589.44. Can we conclude, at the 0.05 significance level, that the population variance of scores of biology majors, σ21, is less than σ22, the population variance of scores of other majors? Perform a one-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

Null Hypothesis: ?

Alternative Hypothesis: ?

Type of test statistic: ? (z, t, chi square, F)

The value of the test statistic: ? (round to 3 decimal places)

The critical value at the 0.05 level of significance: ? (Round to 3 decimal places)

Can we conclude that the variance of all scores of biology majors is less than the variance of all the scores of other majors? (yes or no)

Answer 1

H₀:  σ₁ = σ₂ (There is no variety in scores of biology majors and scores of different majors)

H₁:  σ₁ < σ₂ (There is less change in scores for biology majors than different majors)

Test statistics, F= σ₁²/σ₂² =9101.16/16589.44 = 0.5486

Degrees of fredom ⇒ n₁ − 1 = 24−1 = 23

⇒ n2 − 1 = 23−1 = 22

F critical at df(23, 22), α =0.05 is: 2.03766

The F test statsitic don't fall in critical locale, hence, can't finish up the case.

Answer: No.