Question

A medical researcher says that 24% of adults in a certain country are smokers. In a random sample of 200 adults from that country, 17.5% say that they are smokers. At a 5% level of significance, is there enough evidence to support the researcher’s claim?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.24
Alternative Hypothesis, Ha: p ≠ 0.24

Rejection Region
This is two tailed test, for α = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.175 - 0.24)/sqrt(0.24*(1-0.24)/200)
z = -2.15

P-value Approach
P-value = 0.0316
As P-value < 0.05, reject the null hypothesis.
.

yes,there is enough evidence to support the researcher’s claim