Question

We want to know how medical care costs differ between men and women. Assume medical cost follows a normal distribution. Among the 110 men surveyed, the average medical cost is $7163 with standard deviation $6663. Among the 90 women surveyed, the average medical cost is $6224 with a standard deviation $3277.

(1) Construct the 95% CI for medical care costs for men and women separately. (4 points)

(2) Conduct a hypothesis testing to test whether the medical costs differ between men and women. Assume the two populations have unequal variance. (5 points)

Some critical values for t scores are listed for your reference. You may need to use one of them to get the rejection region:

     

t _{(0.025, 33)} = 2.03 (which means the rejection region is t ≥ 2.03 or t ≤ −2.03)

t _{(0.025, 133)} = 1.98

t _{(0.025, 150)} = 1.98

t _{(0.025, 165)} = 1.97

t _{(0.025, 190)} = 1.97

t _{(0.025, 200)} = 1.97

t _{(0.025, 500)} = 1.96

(3) What statistical conclusions will you make based on the hypothesis testing?

Answer 1

solution:

given data:

• total mens = 110
• total womens= 90
• avarage medical cost for men=$7163
• avarage medical cost for women=$6224
• standard deviation for men= $6663
• standard deviation for women=$3277

1.here we need to find out the 95% CI for medical care cost for men and women

FOR MEN:

from the given data we have the function is t(0.025,133)=1.98

we know the formula is ( avarage medical cost(1.98*standard deviation))

now substitute the given values in the formula,

=(7163(1.98*6663))

=((7163+(1.98*6663)),(7163-(1.98*6663)))

=((7163+13192.74),(7163-13192.74))

=(20355.4,-6029.4)

here the medical care cost for the men is (20355.4,-6029.4).

FOR WOMEN:

here we have the function is t(0.025,150)=1.98

we have the formula is ( avarage medical cost(1.98*standard deviation))

now substitute the given values in the formula,

=(6224(1.98*3277))

=((6224+(1.98*3277)),(6224-(1.98*3277)))

=((6224+6488.46),(6224-6488.46))

=(12712.46, -264.46).

here the medical care cost for the women is (12712.46, -264.46).