Question

The color reference provided by the automotive manufacture is 44.21%. Does this known value match the measured value at the 95% confidence level

Answer 1

Answer:

This known value does not match the measured value at the 95% confidence level.

The 95% confidence interval for value is calculated as 42.92 to 43.78%,

Step-by-step explanation:

The complete question is:

Police have a hit-and-run case and need to identify the brand of red auto paint. The percentage of iron oxide, which gives paint its red color, was determined to be 43.35 ± 0.33% by one method of analysis using five measurements. The color reference provide by the automotive manufacture is 44.21%. What can you conclude about whether the sample matches the reference at a 95% confidence level?

Student's t test is used to compare the two values .

Here n=5

Degrees of freedom =ν= n-1= 5-1=4

The value from t- table for 4 d.f at 95 % confidence interval is 2.776

The test statistic is

x`± t ∝/2(v). S/√n

43.35 ± (2.776)(0.33)/√5

= 43.35 ± 0.43

= 43.78, 42.92

Here the 95% confidence interval for μ calculated is 42.92 to 43.78%, where as color reference provided by the automotive manufacture is 44.21%.

This known value does not match the measured value at the 95% confidence level.