Question

4.b) A jewelry artist has a new shipment of beads that she thinks are of lower quality than she expects from the supplier. To test this suspicion, she takes a random sample from her new stock of beads and finds that 21 beads out of 200 have under-sized holes. Is this good evidence ( a = .05 ) that these beads have a higher proportion of under-sized holes than the shipments with 7% under-sized holes she usually gets?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.07
Alternative Hypothesis, Ha: p > 0.07

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.105 - 0.07)/sqrt(0.07*(1-0.07)/200)
z = 1.94

P-value Approach
P-value = 0.0262
As P-value < 0.05, reject the null hypothesis.

yes, this is good good evidence ( a = .05 ) that these beads have a higher proportion of under-sized holes than the shipments with 7% under-sized holes she usually gets