Final answer:
To determine if the proportion of burglaries through an open or unlocked door or window differs significantly from the stated 30%, a hypothesis test is used, comparing the z-score from the sample data with the critical value at a 0.05 significance level.
Step-by-step explanation:
The question is asking whether the proportion of burglaries in which access was gained through an open or unlocked door or window is significantly different from the stated proportion of 30% in a random sample of 130 burglaries where 85 were not via an open or unlocked door or window. To answer this, we would need to perform a hypothesis test.
The null hypothesis (H0) would state that the proportion is equal to 30% (p = 0.30), and the alternative hypothesis (Ha) would suggest that the proportion is not equal to 30% (p ≠ 0.30).
Using a significance level (alpha) of 0.05, we can compute the z-score and compare it to the critical value to determine whether to reject or fail to reject the null hypothesis.
For this scenario, given the sample size (n = 130) and the sample proportion of burglaries not via an open or unlocked door or window (p' ≈ 0.654), we would calculate the z-score using the formula for a proportion test. If the z-score falls within the critical region, then we would reject H0, otherwise, we would not reject H0.