Question

A police officer wants to know the proportion of crimes that are burglaries within the last five years. She randomly selects 40 records from a database of all crimes and checks their records. She finds that 30% of the crimes were labeled as burglary within the last five years. Select one: a. Yes b. No, because it wasn't a random sample. c. No, because n(p-hat) 10 or níq-hat) 10 d. No, because the sample size wasn't at least 30 and the population wasn't normally distributed. e. No, because we already know the population proportion

Answer 1

Answer:

a. Yes

See explanation below.

Step-by-step explanation:

Assuming that if the question is if we can use the normal approximation for the true proportion.

For this case we have n = 40 and p = 0.3 (probability of success)

We need to check some conditions:

1) Random sample : This condition is satisfied since the problem says that she randomly select 40 records

2) $n \hat p = 40*0.3 =12 \geq 10$

$n(1-\hat p)= 30 *(1-0.3) = 28 \geq 10)$

3) 10% condition: the random sample is assumed to be less than 10% of the original population size (assumed)

The population proportion have the following distribution  

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$  

So then as we can see the normal approximation for this case makes sense since we have all the 3 conditions satisfied so then the answer would be:

a. Yes