Question

You wish to test the following claim (H1H1) at a significance level of α=0.002α=0.002.

      Ho:p=0.15Ho:p=0.15
      H1:p<0.15H1:p<0.15

You obtain a sample of size n=338n=338 in which there are 34 successful observations.

When finding the critical value and test statistic, which distribution would we be using?

• Normal distribution (invNorm for critical value)
• T distribution (invT for critical value)
• χ2χ2 distribution (invχχ for critical value)
• F distribution (invF for critical value)

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.15
Alternative Hypothesis, Ha: p < 0.15

Rejection Region
This is left tailed test, for α = 0.002
Critical value of z is -2.88.
Hence reject H0 if z < -2.88

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.1006 - 0.15)/sqrt(0.15*(1-0.15)/338)
z = -2.54

P-value Approach
P-value = 0.0055
As P-value >= 0.002, fail to reject null hypothesis.

Normal distribution (invNorm for critical value)