Question

During the cold months heating bills can be expensive. A contractor claims that installing a new brand of insulation will considerably lower the average heating bill, which is typically $250. After we collected data for 4 months on a house with the new insulation we found that average heating bill was $220 for a period of 4 months, with standard deviation $30.

1. What is the standard score for the average in our sample?

2. What is the probability that an average heating bill is less than $220?

3. The p-value for this test is:

A. same as p, p = the probability calculated in the previous step.

B. 1-p, p=the probability calculated in the previous step.

C. 2(1-p), p=the probability calculated in the previous step.

D. 2p, p=the probability calculated in the previous step.

Answer 1

SOLUTION 1: The Standard score for the average in our sample is

Z= -30/30/2

Z= -2.00

2)  The probability that an average heating bill is less than $220

P (X<220)=P (Z<−2)

Use the standard normal table to conclude that:

P (Z<−2)=0.0228

Solution 3: The P-Value is .02275. (Using Z table)

A. same as p, p = the probability calculated in the previous step.