The National Institute of Standards and Technology (NIST) supplies a \"standard

Question

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?

Explanation / Answer

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]

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