Question

1- In the nation, about 19% of the population is uninsured. In a recent poll in California, out of 120 people surveyed, 18 had no medical insurance. Is the proportion of uninsured lower in California than in the nation at large? Use alpha=.05.

What would be the critical value (be sure to include the appropriate sign) for this hypothesis test?

2- In the nation, about 19% of the population is uninsured. In a recent poll in California, out of 120 people surveyed, 18 had no medical insurance. Is the proportion of uninsured lower in California than in the nation at large? Use alpha=.05

What would the alternative hypothesis be

3- In the nation, about 19% of the population is uninsured. In a recent poll in California, out of 120 people surveyed, 18 had no medical insurance. Is the proportion of uninsured lower in California than in the nation at large? Use alpha=.05

What is your calculated test statistic that you will use to compare with the critical value above?

4- Forget the real answers above. What if your test statistic is -1.657 and your critical value is -1.799. What should you decide

a. reject the null and determine that the proportion is lower

b. reject the null and determine the proportion could still be 19%

c. do not reject the null and determine the proportion may not have gone down

d. do not reject the null and determine that the proportion has gone down

Answer 1

1)

This is left tailed test, for α = 0.05
Critical value of z is -1.64.
Hence reject H0 if z < -1.64

2)

Alternative Hypothesis, Ha: p < 0.19

3)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.15 - 0.19)/sqrt(0.19*(1-0.19)/120)
z = -1.12

4)

1)

This is left tailed test, for α = 0.05
Critical value of z is -1.64.
Hence reject H0 if z < -1.64

2)

Alternative Hypothesis, Ha: p < 0.19

3)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.15 - 0.19)/sqrt(0.19*(1-0.19)/120)
z = -1.12

4)

d. do not reject the null and determine that the proportion has gone down