Question

According to the federal government, 24% of workers covered by their company’s health care plan were not required to contribute to the premium (Statistical Abstract of the UnitedStates: 2006). A recent study found that 81 out of 400 workers sampled were not required to contribute to their company’s health care plan. Has the percent of workers not required to contribute to their company’s health plan decreased? Test at the 99% confidence level.

1. State the null and alternative hypotheses.

2. Specify alpha based on the confidence level indicated.

3. Use alpha to develop the critical value that delineates the rejection region.

4. Compute the test statistic

5. Calculate P-value based on test statistic.

6. Compare the test statistic to the critical value. Compare the P-value to alpha.

7. Based on your comparisons identify your decision.

8. Indicate the conclusion for the scenario

Answer 1

1) Null and alternative hypotheses

Ho : p = 0.24

H1 : p < 0.24

2) level of significance a = 0.01

3) critical value for a= 0.01 and left tailed test

Zcritical = Z​​​​​​a = Z​​​​​​0.01

Zcritical = - 2.33

4) test statistic Z

Z = (p^ - p)/sqrt [ p*(1-p)/n ]

Where p^ = 81/400 = 0.203

Z = (0.203 - 0.24)/sqrt[ 0.24*0.76/400]

Z = -1.73

5) p-value = P( Z < -.173)

p-value = 0.0418

6) Ztest = -1.73 > -2.33

p-value = 0.0418 > 0.01

7) Decision : fail to reject the null hypothesis Ho

8) conclusion : There is not sufficient evidence to conclude thatpercent of workers not required to contribute to their company’s health plan is decreased