Question

Trapspacing measurements (in meters) for a sample of seven terms of red spiny lobster fishermen are reproduced as following: 93, 99, 105, 94, 82, 70, 86. Suppose you want to determine if the true value of ? differs from 95 meters.

Answer 1

Let be the average of trapspacing measurements

We want to determine if the true value of differs from 95 meters. That means we want to test the following hypotheses using one sample test for means

We have the following sample information

n=7 is the sample size

The sample mean is

The sample standard deviation is

We will estimate the population standard deviation using the sample

the standard error of mean is

The sample size n=7 is less than 30 and the population standard deviation is not known. Assuming that the population of Trapspacing measurements have a normal/approximately normal distribution, we will use t- statistics to test the hypotheses.

The hypothesized value of is

The test statistics is

The degrees of freedom for t statistics is n-1 = 7-1 =6

The critical value of t for significance level of 0.05 is

using the standard t tables we get

We will accept the null hypothesis if the test statistics is belwteen -2.447 and +2.447.

Since the test statistics of -1.17 is between -2.447 and +2.447, we do not reject the null hypothesis.

We conclude that there is no sufficient evidence to support the claim that the true value of differs from 95 meters.

That means we can say that the true value of does not differ from 95 meters.