Question

6. The Police-Public Contact Survey (PPCS) asks respondents who have been stopped by the police while driving a vehicle how many officers were on the scene during a stop. Female stopped drivers (n=2,033) reported a mean of 1.24 (s=.27) officers. Construct a 95% confidence interval around this sample mean and interpret the interval in words. What would the 90% confidence interval be? (6pts total; 2pt CI, 1pt interpretation)

1. 95% Confidence Interval:

2. Interpretation:

3. 90% Confidence Interval:

4. Interpretation:

Answer 1

Sample size is very large we will use Z critical value for finding confidence interval

sample Mean = 1.24
Z critical = 1.96
s_M = √(0.27²/2033) = 0.01
μ = M ± Z(s_M)
μ = 1.24 ± 1.96*0.01
μ = 1.24 ± 0.0117

95% CI [1.2204, 1.2596].

Interpretation:You can be 95% confident that the population mean (μ) of officers during scene falls between 1.2204 and 1.2596.

Sample Mean = 1.24
Z critical = 1.65
s_M = √(0.27²/2033) = 0.01
μ = M ± Z(s_M)
μ = 1.24 ± 1.65*0.01
μ = 1.24 ± 0.0165

90% CI [1.2235, 1.2564].

Interpretation: You can be 90% confident that the population mean (μ) of officers during scene falls between 1.2235 and 1.2565.