Question

Provide an appropriate response.

Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 4000 citizens yielded 2250 who are in favor of gun control legislation.

a) Show that this situation meets the necessary criteria to calculate the confidence interval for the proportion.

b) Estimate the true proportion of all Americans who are in favor of gun control legislation using a 90% confidence interval. Round your result to three decimal places.

c) Based on the interval can you say that less than 55% of Americans favor gun control legislation? Why or why not?

Answer 1

a) Since the sample size is more than 30, hence this can be approximated to normal.

hence the criteria is sufficient

b)

We need to construct the 90% confidence interval for the population proportion. We have been provided with the following information about the number of favorable cases:

Favorable Cases X =	2250
Sample Size N =	4000

The sample proportion is computed as follows, based on the sample size N = 4000 and the number of favorable cases X = 2250

The critical value for α=0.1 is z_c =1.645. The corresponding confidence interval is computed as shown below:

CI = (0.55, 0.575)

c)

Since the 90% confidence interval includes the value 0.55

hence we can say that 55% of Americans favor gun control legislation