Question

A distributor of personal computers has five locations in a city. In the year's first quarter, the sales in units were: Location Observed Sale ( units) Northside 70 Pleasant Township 75 Southwick 70 I-90 50 Venice Avenue 35 Total 300 For a goodness-of-fit test that sales were the same for all locations, what is the critical value at the 0.01 level of risk? Select one: a. 7.779 b. 15.033 c. 13.277 d. 5.412

Answer 1

The critical value for a goodness-of-fit test with 4 degrees of freedom at the 0.01 level of risk is 13.277, which corresponds to option c.

Step-by-step explanation:

The question asks for the critical value at a 0.01 level of risk for a goodness-of-fit test that assumes sales were the same for all locations. When performing a goodness-of-fit test, we use the chi-square distribution to find the critical value. The degrees of freedom (df) in our case is the number of categories minus 1, which would be 5 - 1 = 4. Looking at a chi-square distribution table at the 0.01 significance level (1% level of risk) with 4 degrees of freedom, we will find the critical value for this statistic.

By consulting the table, the critical value is 13.277. Therefore, option c is the correct answer.

Answer 2

The correct option is (c) 13.277.

Step-by-step explanation:

The observed data is:

Location Observed sales (units)

Northside 70

Pleasant Township 75

Southwick 70

I-90 50

Venice Avenue 35

TOTAL 300

The test statistic for the Goodness of fit test is:

`\chi^(2)=\sum((Observed-Expected)^(2))/(Expected)`

For k independent samples this test statistic follows a Chi-square distribution with degrees of freedom (k - 1).

The sample size in this case is, k = 5.

The degrees of freedom is, (k - 1) = 4.

The level of significance is, α = 0.01.

The critical value of the test is:

`\chi^(2)_(\alpha ,k-1)=\chi^(2)_(0.01,4)=13.277`

**Use the Chi-square table.

Thus, the critical value is 13.277.