A Senate Committee Is Studying the Cost of Health Care

question 16

Essay

A Senate committee is studying the cost of health care and is interested in the relationship between y = the monthly premium paid, x₁ = the age of the policy holder, and x₂ = the number of dependents on the policy. Partial computer output for the Senate study is given below. The regression equation is Prem = 177 + 1.3 x₁ + 68 x₂ ​ S = 17.25 R-sq = 59.1% ​ Use a significance level of .05 for all tests requested.
a) Calculate and interpret a 95% confidence interval for β₂.
b) Does the model appear to be useful? Test the relevant hypothesis.
c) Conduct a test for the following pair of hypotheses: H₀ : β₁ = 0 vs. β₁ ≠ 0.
d) Based on your result in part (c), would you conclude that the age of the policy holder is an important variable? Explain your reasoning.
e) An estimate of the mean monthly premium for a policy holder 23 years old with 2 dependents is desired. Compute a 90% confidence interval for α + β₁(23) + β₂(2) if the estimated standard deviation of a + b₁(23) + b₂(2) is 35. Interpret the resulting interval.
f) A single individual, 23 years old with 2 dependents, is identified. Predict the monthly premium for this person using a 90% interval.

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Definitions:

Stretching Frequency

A term used in vibrational spectroscopy to describe the rate at which a bond between atoms vibrates, often measured in wave numbers (cm^-1).

Broad Absorption

In spectroscopy, it indicates a wide range of wavelengths over which a substance absorbs electromagnetic radiation.

IR Absorption

A technique used to identify and study chemicals by measuring the absorption of infrared radiation at different wavelengths.

IR Spectroscopy

A technique used for identifying and studying chemicals by analyzing the infrared light absorbed, emitted, or scattered by the sample.