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

Answer:

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:

$\chi^{2}=\sum\frac{(Observed-Expected)^{2}}{Expected}$

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.