Question

Vicki wishes to compare two varieties of seeds with regard to their germination rates. Brand 1 advertises that it has the highest germination rate amongst all seeds of this type. Brand 2 makes no such claim. Write p₁ and p₂ for the true germination rates of seed of Brand 1 and Brand 2 respectively. Vicki wants to test H₀: p₁ = p₂ vs H₁: p₁ > p₂.

If 179 out of 200 seeds of Brand 1 germinated, and 153 out of 180 seeds of Brand 2 germinated, what decision should Vicki reach?

[Hint: Compute the test statistic and compare it with various critical values. Or, you can use R Commander.]

		reject H0 at the 10% and 5% levels of significance, but not at the 2.5% or 1% levels of significance.
		reject H0 at the 10%, 5%, 2.5% and 1% levels of significance.
		not reject H0 at any of the 10%, 5%, 2.5% or 1% levels of significance.
		reject H0 at the 10% level of significance, but not at the 5%, 2.5% or 1% levels of significance.
		reject H0 at the 10%, 5% and 2.5% levels of significance, but not at the 1% level of significance.

Answer 1

Hypotheses : To test null hypothesis H. : P1 - P2 = 0 against alternative hypothesis H1 :P1 - P2 > 0 Let P1, 2 denote the respective sample proportions and n1, n2 denotes the sample sizes respectively. Here, Pi = 0.8950, n1 = 200, p2 = 0.8500, n2 = 180 The test statistic can be written as: (p1 -P2) – 0 P1*(1-P) P2*(1-P2) + ni n2 which under H, follows a standard normal distribution. Decision rule / Rejection region : We reject H, at 0.1 level of significance if P-value < 0.1 or if Zobs > 20.1 = 1.281552 0.4 0.3 0.2 0.1 0.0 Now, The value of the test statistic Zobs = 1.310996 1.31 (0.895 – 0.850) 0.895*(1-0.895) 0.850*(1-0.850) + 200 180 V The critical value = 1.281552 1.28 P-value = P(Z > Zobs) = P(Z <1.310996) = (1 - 0.905070) = 0.094930 – 0.0949 Conclusion : Since p-value < 0.1 and 2 > Zcritical = 1.281552, so we reject Ho at 0.1 level of significance Hence, we can conclude that the first population proportion is significantly greater than second population proportion.

ans-> iv) reject H0 at the 10% level of significance, but not at the 5%, 2.5% or 1% levels of significance.