A doctor claims that the number of births by day of the week...

A doctor claims that the number of births by day of the week is uniformly distributed. To test the claim, you randomly select births from a recent year and record the day of the week the birth takes place. Use a 10% significance to test the claim. Round to the fourth as needed. Categories | Observed Frequency | Expected Frequency Sunday | 59 Monday | 46 Tuesday | 47 Wednesday | 40 Thursday | 54 Friday | 60 Saturday | 56 Test Statistic: Degrees of Freedom: p-val: Decision Rule: Select an answer Did something significant happen? Select an answer There Select an answer enough evidence to conclude Select an answer

Transcript

00:01 Okay, so here we've got a kye square question.

00:06 So we've got a table with observed values, and we want to test the hypothesis that the birth by day of the week is uniformly distributed compared to not uniformly distributed.

00:19 And to do this, we're just going to compute our kai squared test statistic, which is given by the sum of all the observed values minus the expected values squared, divided by the expected values, where i goes from one to seven for each of the days of the week.

00:40 Now, the expected values are the values it would take under the uniform distribution, and that is just going to be the total frequency divided by seven, right? because there are seven days, and so the expected value for each day is going to be the total frequency divided by the number of days so that each of them would have the same expected value that's what uniform distribution is and the total frequency you can find is 362 so the expected value is 362 over 7 so the kai squared statistic is going to be plugging this in and the oi values in to here so for example the first one is going to be at 59 minus 362 over 7 squared divided by 362 over 7 plus and so on and so on, up until the last one, which is 56, minus 362 over 7 squared over 362 over 7.

01:49 And then remember to divide them all.

01:53 Now, usually you'd have to divide, oh, sorry, no, i've already done that, never mind.

01:58 So that would be our kai squared statistic, and if you plug in all those numbers, you'll find that it's 5 .85 to 2 decimal places.

02:08 Oh, they want it to 4 decimal places.

02:10 So it's 5 .856 to 4 decimal places.

02:14 They then ask for the degrees of freedom.

02:17 The degrees of freedom in a kai square test is just the number of categories you've got minus 1...

Question

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