Respuesta :
Correct question is;
The claim is that the proportion of adults who smoked a cigarette in the past week is less than 0.35, and the sample statistics include n = 1168 subjects with 385 saying that they smoked a cigarette in the past week. Find the value of the test statistic
Answer:
Test statistic is z = -1.46
Step-by-step explanation:
Let's first of all define the hypotheses:
Null hypothesis:
H0: p = 0.35, i.e 35% in the sample of 1,168 adults have smoked cigarettes in the previous week.
Alternative hypothesis:
Ha: p < 0.35, i.e less than 35% in the sample of 1,168 adults have smoked cigarette in the previous week.
The sample size is, n = 1,168 while the number of adults who smoked in the previous week would be; x = 385
Therefore, the sample proportion of adults who smoked in the previous week would be calculated as;
p^ = x/n = 385/1168 ≈ 0.3296
Now, from Central Limit Theorem for large samples, The sampling distribution of the sample proportion p^, will have a mean of μ = p = 0.35
Formula for standard deviation is;
σ = √[p (1 – p)/n]
σ = √(0.35 × (1 – 0.35)/1168)
σ = √0.0001947774
σ = 0.014
Formula for test statistic is;
z = (p^ - p)/σ
z = (0.3296 - 0.35)/0.014
z = - 1.46
