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

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.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.