Question

​(a) Write the claim mathematically and identify Upper H 0 and Upper H Subscript a. ​(b) Find the critical​ value(s) and identify the rejection​ region(s). (c) Find the standardized test statistic.​ (d) Decide whether to reject or fail to reject the null hypothesis. A medical researcher says that at least 24​% of adults are smokers. In a random sample of 160 ​adults, 22.5​% say they are smokers. At alphaequals0.03​, do you have enough evidence to reject the​ researcher's claim?

Answer 1

Sample size (n) = 160

= 0.225

1. The hypotheses are

H₀: p ≥ 0.24

H_a: p < 0.24

2. One sided z critical values at α = 0.03 is Z_α = Z_0.03 = -1.88

3. Test statistics: Z = ( – P₀) / √ (P₀ (1 - P₀) / n)

                           Z = (0.225 – 0.24) / √ ((0.24)*(1-0.24)/160)

                           Z = -0.444

4. Decision rule: Reject H₀ if |Z| < -1.88.

Using critical value approach, Z = -0.444 > Z₀ = -1.88. Since test statistics is not lies in rejection region so we failed to reject null hypothesis at 0.03 level of significance.

5. Conclusion: Failed to reject H₀. There is not enough evidence to claim that A medical researcher says that less than 24% of adults are smokers at the 0.03 level of significance.