Use the given categorical data to construct the relative frequency distribution. natural births randomly selected from four hospitals in a highly populated region occurred on the days of the week (in the order of monday through sunday) with the frequencies 52, 64, 71, 57, 57, 46, 53. 1. does it appear that such births occur on the days of the week with equal frequency? construct the relative frequency distribution. day relative frequencymonday %tuesday %wednesday %thursday %friday %saturday % sunday %(type integers or decimals. round to two decimal places as needed.)

Day                     Relative Frequency

Monday             52/400=0.13 = 13%

Tuesday            64/400=0.16=16%

Wednesday       71/400=0.1775=17.75%

Thursday            57/400=0.1425=14.25%

Friday                 57/400=0.1425=14.25%

Saturday            46/400=0.115=11.5%

Sunday               53/400=0.1325=13.25%

Total                        1.00=100%

After we see the results obtained we can conclude that the relative frequencies are very similar for each day analyzed. But in order to have a precise answer is possible to use a chi square test.

Now we can calculate the degrees of freedom for the statistic given by:

And we can calculate the p value given by:

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(1.78,6,TRUE)"

Since the p value is higher than any significance level we FAIL to reject the null hypothesis at 5% of significance, and we can conclude that such births occur on the days of the week with equal frequency.

Step-by-step explanation:

Data given

Day              Frequency

Monday             52

Tuesday            64

Wednesday       71

Thursday            57

Friday                 57

Saturday            46

Sunday               53

The first step on this case is find the total sum of frequencies given by:

52+64+71+57+57+46+53=400.

A relative frequency is "the fraction of times an answer occurs. To find the relative frequencies, we just need to divide each frequency by the total number", and we can express it as % or as fraction.

If we apply this definition and we find the relative frequencies we have:

Day                     Relative Frequency

Monday             52/400=0.13 = 13%

Tuesday            64/400=0.16=16%

Wednesday       71/400=0.1775=17.75%

Thursday            57/400=0.1425=14.25%

Friday                 57/400=0.1425=14.25%

Saturday            46/400=0.115=11.5%

Sunday               53/400=0.1325=13.25%

Total                        1.00=100%

We can check the operations with the total, if the total is not equal to 1 we need to review the calculations since the total sum needs to be 1 or 100%.

After we see the results obtained we can conclude that the relative frequencies are very similar for each day analyzed. But in order to have a precise answer is possible to use a chi square test.

The statistic to check the hypothesis is given by:

The expected frequencies for each day would be 100%/7 =14.286%

Now we can calculate the degrees of freedom for the statistic given by:

And we can calculate the p value given by:

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(1.78,6,TRUE)"

Since the p value is higher than any significance level we FAIL to reject the null hypothesis at 5% of significance, and we can conclude that such births occur on the days of the week with equal frequency.

it is a reproduction.

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