A health study involves 920 randomly selected deaths with...

A health study involves 920 randomly selected deaths, with 345 of them caused by heart disease (based on CDC data). Use this data as a pilot study to estimate the proportion of all deaths caused by heart disease. Find minimum required sample size to within 0.04 with a 99% confidence.

Transcript

00:01 So our question says a health study involved 920 randomly selecting debt with 345 of them caused by heart diseases.

00:07 So you're supposed to use this data as a pilot study to estimate the proportion of all debt caused by heart disease.

00:14 Then we are also asked to find a minimum required sample size to within 0 .04 with 99 % confidence interval.

00:22 So let's start with the first question because it's looking like, not even it's looking like we actually have two questions right here.

00:27 Are supposed to estimate the proportion and also find a minimum required sample size so uh the sample size as a whole end is equals to 920 and out of this 920 out of the 920 the fraction of of people that had a heart disease is actually 345 so that's 345 so the sample proportion pickup which is the estimates of the proportions of all debts caused by heart diseases is actually going to be 345 divided by 920 so let's pick a calculator and get the value of 345 divided by 920 so we have 345 and our answer is 0 .375 so the proportion of people that died by heart this is actually 0 .3 and that is the estimate of the proportion of people that died by heart this is so that's our first question pickup is actually 0 .375 so the second question stays are finding minimum sample size to within 0 .04 with 99 % confidence in so far so second question our margin of error is actually 0 .04 we're looking for the sample size estimates of the population proportion the sample proportion rather is still 0 .375 and then that means our cue is going to be 1 minus 0 .375 which is going to be 0 .625 the question says we should be 99 % confidence that means our confidence level better is going to be 99 % so at 99 % confidence in time the formula for the margin of error m is given as a critical value times the square root of p -cap q -cab divided by n critical value in this case is going to be a z score and at 99 % confidence in our the critical value is going to be having a value of 2 .45.

02:26 So let's substitute our parameters.

02:29 So we have the margin of error to be 0 .04 is equal to 2 .45 times we have the square root of 0 .375 times 0 .625 divided by n.

02:46 So we have 0 .04 is equals to 2 .45 times.

02:48 So we have 0 .04 .04 is equals to 2 .45 times...

Question

A health study involves 920 randomly selected deaths, with 345 of them caused by heart disease (based on CDC data). Use this data as a pilot study to estimate the proportion of all deaths caused by heart disease. Find minimum required sample size to within 0.04 with a 99% confidence.

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