Question

In: Statistics and Probability

Historical records show that in 1960 the average household size with 3.29 people with a standard...

Historical records show that in 1960 the average household size with 3.29 people with a standard deviation of 1.20 people in 2017 a sample 25 households in Richmond Virginia showed and mean number of residents per house where were 3.91 at a 0.1 significance level is it reasonable to conclude the mean number of residents in Richmond Virginia today is different from the typical American household in 1960?

a. in the above problem, the critical values are
(round to four decimal places as needed)

b. compute the value of the statistic
(round to four decimal places as needed)

Expert Solution

Objective: To test whether the mean number of residents in Richmond Virginia today is different from the typical American household in 1960.

Let denote the mean number of residents in Richmond Virginia today. The Null and Alternative Hypothesis can be expressed as follows:

Vs at

As mentioned in the problem, since, the population standard deviation is unknown, the appropriate test to test the above hypothesis would be a one sample t test:

But before running this test, we must ensure that the data satisfies the assumptions of this test:

- The data is continuous - The observations are independent - The data is normally distributed - There are no outliers

Assuming that all the assumptions are satisfied:

The test statistic is given by:

with critical region given by: for two tailed test.

a.

The critical value of t is given by:

Using excel,

We get

b.

From the given data,

Substituting the values obtained in the test statistic:

= -2.5833

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Etin TINV Returns the inverse of the Student's t-distribution

TINV(0.10,24 TINV(probability, deg_freedom)

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orchestra answered 2 years ago

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