QuestionBelow is a hypothesis test. Label the different parts of the test in the boxes.
A hospital director is told that of the treated patients are uninsured. The director wants to test the claim that the percentage of uninsured patients is over the expected percentage. A sample of 400 patients is found that 200 were uninsured. At the 0.02 level, is there enough evidence to support the director's claim?
Studdy Solution
STEP 1
1. The null hypothesis is that the proportion of uninsured patients is less than or equal to 47%.
2. The alternative hypothesis is that the proportion of uninsured patients is greater than 47%.
3. The sample size is 400.
4. The sample proportion is 0.5 (since 200 out of 400 patients are uninsured).
5. The level of significance is 0.02.
STEP 2
1. Define the hypotheses.
2. Calculate the test statistic.
3. Determine the critical value and decision rule.
4. Make a decision based on the test statistic and critical value.
STEP 3
Define the hypotheses:
- Null hypothesis:
- Alternative hypothesis:
STEP 4
Calculate the test statistic using the formula:
Substitute the values:
STEP 5
Determine the critical value for a one-tailed test at the 0.02 level of significance.
For a significance level of 0.02 in a right-tailed test, the critical value is approximately 2.05 (from Z-tables).
STEP 6
Make a decision:
- Compare the test statistic with the critical value .
- Since , we do not reject the null hypothesis.
Conclusion: There is not enough evidence at the 0.02 level of significance to support the director's claim that the percentage of uninsured patients is over 47%.
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