Here are 6 measurements of the electrical conductivity of an iron rod: 10.08 9.8

Question

Here are 6 measurements of the electrical conductivity of an iron rod:

10.08 9.89 10.05 10.16 10.21 10.11

Data Set

The iron rod is supposed to have conductivity 10.1.

Do the measurements give good evidence that the true conductivity is not 10.1?

The 6 measurements are an SRS from the population of all results we would get if we kept measuring conductivity forever.

This population has a Normal distribution with mean equal to the true conductivity of the iron rod and standard deviation 0.1.

Use this information to carry out a test, following the four-step process as illustrated in Example 17.7.

Step 1:

STATE: What is the practical question that required a statistical test?

Is there evidence that the true conductivity of the iron rod is 10.1?

Is there evidence that the true conductivity of the iron rod is larger than 10.1?

Is there evidence that the true conductivity of the iron rod is not 10.1?

Does this sample give a good estimate for the true conductivity of the iron rod?

Step 2:

PLAN: Identify the parameter.

The parameter is the true conductivity.

The parameter is the population standard deviation.

The parameter is the sample mean.

The parameters are the sample mean and standard deviation.

The parameter is the average of all the sample means with n = 6.

Step 3:

PLAN (continued): State the null and alternative hypotheses.

H 0: = 10.1 vs. Ha: 10.1

H 0: = 10.1 vs. Ha: < 10.1

H0: 10.083

H 0: x = 10.1 vs. Ha: x 10.1

H 0: = 10.1 vs. Ha: > 10.1

Step 4:

SOLVE: Assume that we have an SRS from a Normal population.

Calculate the test statistic and give your answer to 2 decimal places.

Fill in the blank:

Step 5:

SOLVE (continued): What is the P-value for the test?

0.68

0.44

0.11

0.56

Step 6:

Conclude: Which is an appropriate conclusion for this test?

We reject the null hypothesis and conclude the true conductivity is not different from 10.1.

We do not reject the null hypothesis and conclude the true conductivity is not 10.1.

We do not reject the null hypothesis and conclude the true conductivity is not different from 10.1.

We reject the null hypothesis and conclude the conductivity is different from 10.1.

Is there evidence that the true conductivity of the iron rod is 10.1?

Is there evidence that the true conductivity of the iron rod is larger than 10.1?

Is there evidence that the true conductivity of the iron rod is not 10.1?

Does this sample give a good estimate for the true conductivity of the iron rod?

Explanation / Answer

Is there evidence that the true conductivity of the iron rod is not 10.1?

The parameter is the true conductivity.

H 0: = 10.1 vs. Ha: 10.1

------------------------

df = 5

p value =

0.68

We do not reject the null hypothesis and conclude the true conductivity is not different from 10.1.

Mean 10.08333 std dev 0.110574 std error 0.045142

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