Question

The uninsured rate before the Affordable Care Act (ACA) was passed in 2010 was 15.7%. A skeptic believes that as a result of ACA some people who were on private insurance have now switched to government care, but the overall uninsured rate has remained the same. In order to test this claim he takes a random sample of 168 individuals and finds that 17 of them are currently uninsured. Is there enough evidence to support the skeptic’s claim?

Set up the null and alternate hypotheses.

Compute an appropriate test statistic.

What is the p-value? What do you conclude at α=0.01? Explain

Answer 1

1)

Hypothesis-

H0: p = 0.157

Ha: p 0.157 (Two tailed)

2)

Test statistics

Sample proportion = 17 / 168 = 0.1012

z = - p / sqrt( p(1-p) / n)

= 0.1012 - 0.157 / sqrt(0.157 * 0.843 / 168)

= -1.99

This is test statistics value

3)

p-value -

p-value = 2 * P( Z < z) ( 2 is multplied to probability since this is two tailed test)

= 2 * P( Z < -1.99)

= 2 ( 1 - P (Z < 1.99 ) )

= 2 * ( 1 - 0.9767 )

= 0.0466

Since p-value > 0.01 significance level, we do not have sufficient evidence to reject H0.

We conclude at 0.01 level that we fail to support the claim.