Question

A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days. Frequency Mon 25 Tue 22 Wed 19 Thu 18 Fri 16 Total 100 Assuming that a goodness-of-fit test is to be conducted using a 0.10 level of significance, the critical value is:

Answer 1

The degrees of freedom are given by;

`df =n-1= 5-1=4`

The significance level is 0.1 so then the critical value would be given by:

`F_(cric)= 7.779`

If the calculated value is higher than this value we can reject the null hypothesis that the arrivals are uniformly distributed over weekdays

Explanation:

For this case we have the following observed values:

Mon 25 Tue 22 Wed 19 Thu 18 Fri 16 Total 100

For this case the expected values for each day are assumed:

`E_i = (100)/(5)= 20`

The statsitic would be given by:

`\chi^2 = \sum_(i=1)^n ((O_i-E_i)^2)/(E_i)`

Where O represent the observed values and E the expected values

The degrees of freedom are given by;

`df =n-1= 5-1=4`

The significance level is 0.1 so then the critical value would be given by:

`F_(cric)= 7.779`

If the calculated value is higher than this value we can reject the null hypothesis that the arrivals are uniformly distributed over weekdays