Question 1: Hypothesis Test for a Population Proportion

According to the Government Accountability Office, 80% of all college students (ages 18 to 23) had health insurance in 2006. The Patient Protection and Affordable Care Act of 2010 allowed young people under age 26 to stay on their parents' health insurance policy. Has the proportion of college students (ages 18 to 23) who have health insurance increased since 2006? A survey of 800 randomly selected college students (ages 18 to 23) indicated that 83% of them had health insurance. Use a 0.05 level of significance.

Step 1: Determine the hypotheses.

Null hypothesis:H₀:p ________

Alternative hypothesis: H_a:p ________

Step 2: Find the mean and standard deviation.

Using Mean =np

Standard deviation:

Step 3: Calculate z- Value.

Step 4: Find the p-value (or probability value area under the curve) for the above Z using

the Z-table or your calculator.

Step 5: State a conclusion.

Question 2:Hypothesis Test when Population Standard Deviation is Unknown

The hospital administrator mentioned that arandomly selected 64 patients and measured the time (in minutes) between when they checked in to the ER and the time they wererstseen by a doctor.The average time is 137.5 minutes and the standard deviation is 39 minutes. She is getting grief from her supervisor on the basis that the wait times in the ER has increased greatly from last year's average of 127 minutes. However, she claims that the increase is probably just due to chance.

Using a significance level of= 0 .05, is the change in wait times statistically significant? Use a two-sided T-test since it seems the supervisor had to inspect the data before she suggested an increase occurred.

Step 1: Determine the hypotheses.

Null hypothesis:H₀:_________

Alternative hypothesis: H: 127

Step 2: Find the criticaltvalue (from the Student's t-table or from calculator):

Step 3: Calculate the test statistic, t_c .

Step 5: State a conclusion.