Figure 4.15 shows a randomization distribution for testing H₀: p = 0.3 vs H_a: p < 0.3. In each case, use the distribution to decide which value is closer to the p-value for the observed sample proportion.

Figure 4.15

(a) The p-value for p̂ = 0.25 is closest to: 0.001 or 0.30?

(b) The p-value for p̂ = 0.15 is closest to: 0.04 or 0.40?

(c) The p-value for p̂ = 0.35 is closest to: 0.30 or 0.70?

A randomization distribution based on 1000 simulated samples is given along with the relevant null and alternative hypotheses. Which p-value most closely matches the observed statistic?

100 80 60 40 20 0.50 0.40 0.60 0.10 0.20 0.30 Sample proportlons Frequency