Question

The health plan at a state university was updated in order to comply with provisions of the Affordable Care Act (ACA). The vision benefit at that university had in previous plan years had to be changed from a comprehensive eye exam to vision test only exam in order to align our preventive benefits with ACA guidelines. The result of this required change was not satisfactory to the university since it considers preventive vision screening crucial to early detection of many other diseases and health issues. So in order to offer annual comprehensive eye exams, we the university worked with the insurance company to add coverage for this important preventive exam with a $10 co-pay. A faculty was interested in the cost the vision centers in the state were charging for such comprehensive eye exams for someone without vision insurance. Having consulted with the HR department on the campus, the faculty was told that the average cost should be around $100. The faculty studied the cost of 16 randomly chosen eye centers and found a mean cost of $114 with a standard deviation of $5. The faculty concluded that the average cost exceeds the value quoted by the HR personnel. Assume that the cost is normally distributed.

Step 1 of 5: The hypotheses for the test will be

A) H₀:  μ  ≤  100, H₁: μ  >  100

B) H₀: μ ≥  100, H₁: μ  <  100

C) H₀: μ  <  100, H₁: μ  ≥  100

D) H₀: μ = 100, H₁: μ   ≠  100

Step 2 of 5: At  α = 0.05, the critical value for a right-tail test of her hypothesis is

A) 1.7531

B) 2.9467

C) 2.1315

D) 1.6449

Step 3 of 5: The value of the test statistic for the hypothesis is

A) 10.4766

B) 10.8444

C) 11.2000

D) 0.0000

Step 4 of 5: The p-value for the appropriate test of the hypothesis is

A)  1.0000

B) 0.0000

C) 0.0500

D) between 0 .01 and 0.05

Step 5 of 5: What will be the decision for the test at a significance level of 0.05?

A) Conclude that average cost is less than $100

B) Not enough information is given to make a decision

C) Do not reject the null hypothesis

D) Reject the null hypothesis and conclude that the average cost at these vision centers in the state for a comprehensive eye exam is greater than $100

Answer 1