The National Institute of Standards and Technology NIST supp

The National Institute of Standards and Technology (NIST) supplies a \"standard liquid\" whose electrical conductivity is supposed to be exactly 5. Is there reason to think that the true conductivity of a shipment of this liquid is not 5?

To find out, NIST measures the conductivity 6 times. Repeated measurements of the same thing vary, which is why NIST makes 6 measurements. These measurements are an SRS from the population of all possible measurements. This population has a Normal distribution with mean ? equal to the true conductivity and standard deviation ? = 0.2.

Make a sketch of the Normal curve for this distribution. (Draw a Normal curve, then mark on the axis the values of the mean and 1, 2, and 3 standard deviations on either side of the mean.) Choose the correct graph:

A.

B.

The National Assessment of Educational Progress (NAEP) gave a test of basic arithmetic and the ability to apply it in everyday life to a sample of 840 men 21 to 25 years of age. Scores range from 0 to 500; for example, someone with a score of 325 can determine the price of a meal from a menu. The mean score for these 840 young men was x = 272. We want to estimate the mean score ? in the population of all young men. Consider the NAEP sample as an SRS from a Normal population with standard deviation ? = 60.

According to the 95 part of the 68-95-99.7 rule, 95% of all values of x¯ with a sample size of 840 fall within ____ on either side of the unknown mean ?. What is the missing number? if you get 2.07 it\'s wrong?

Solution

1. For the first problem, the markings on the normal curve should have been

4.4 4.6 4.8 5.0 5.2 5.4 5.6

but I could not see a graph with such markings. This is so because sigma = 0.2.

2.

95% of values fall between 2 standard error. Here,

Sx = sigma/sqrt(n) = 60/sqrt(840) = 2.0702

However, as we need to standard errors,

2 Sx = 4.1404 [ANSWER, second problem]