Question

Looking at statistics to estimate parameters (Variability not considered)

Suppose the city interview 100, randomly selected, bicyclists that were involved in accidents that were on roadways without bike lanes and 100 bicyclists that were involved in accidents that were on roadways with bike lanes. They found that from the accidents on roadways without bike lanes 27% of the accidents resulted in a trip to the ER, of the accidents on roadways with bike lanes 13% of the accidents resulted in a trip to the ER.

1. Using only the statistics above does there appear to be much difference in the parameters of interest?

2. What do we call the change in the statistic from sample to sample?

3. Next suppose that the city took 30 random samples, each of size 100 of bicyclists that were involved in accidents that were on roadways without bike lanes. From each sample they calculated a statistic. They create a sampling distribution using the statistics. Where do we expect the sampling distribution to be centered (i.e. the mean)? Hint: You will describe the value using words not numbers.

Answer 1

(1)

n1 = 100

p1 = 0.27

n2 = 100

p2 = 0.13

Q = 1 - P = 0.8

Test statistic:

Z = (p1 - p2)/SE

= (0.27 - 0.13)/0.0566 = 2.4735

Take = 0.05

From Table, critical values of Z = 1.96.

Since calculated value of Z is greater than critical value of Z, Reject H0.

Conclusion:

The data support the claim that there appears to be much difference in the parameters of interest.

(2) The change in the statistic from sample to sample is called Standard Error.

(3) We expect the sampling distribution to be centred (i.e., the mean) at , the population mean.