Vitamin d whether ingested as a dietary supplement or...

Vitamin D, whether ingested as a dietary supplement or produced naturally when sunlight falls upon the skin, is essential for strong, healthy bones. The bone disease rickets was largely eliminated during the 1950s, but now there is concern that a generation of children more likely to watch TV or play computer games than spend time outdoors is at increased risk. A recent study of 3400 children randomly selected found 21% of them deficient in vitamin D. Construct a 98% confidence interval for the true proportion of children who are deficient in vitamin D. Select the correct choice below and fill in any answer boxes within your choice.

Transcript

0:00 Hello everyone.

00:01 So in this question we have given out of 3 ,400 children randomly selected and found that 21 % of them deficient in vitamin d.

00:09 Now we need to construct 98 % confidence interval for true proportion of children who are deficient in vitamin d.

00:17 So from the above information, sample size that is n is equal to 3 ,400.

00:24 And here sample proportion is given which is equal to 21 % or.

00:30 We can say that 0 .21 and confidence level that is c is equal to 98 % or we can say that 0 .98.

00:41 Now we can find the significance level and we know that the formula for finding the significance level is alpha is equal to 1 minus confidence level.

00:54 So here alpha is equal to 1 minus 0 .98 and on subtraction we will get equal to 1 minus 0 .98.

00:58 And on subtraction we will get equal.

01:00 To 0 .02.

01:03 Now if alpha is 0 .02 then alpha divided by 2 is equal to 0 .02 divided by 2 which is equal to 0 .01.

01:13 Now we will find the critical value from the z table.

01:17 So the critical value that is z alpha divided by 2.

01:25 So this is equal to z 0 .01 is equal to 2 .1 is equal to 2.

01:31 326.

01:32 Now we will find the confidence interval and we know that the formula for finding the confidence interval for the true proportion is equal to sample proportion plus minus z alpha divided by 2 multiplied by square root of sample proportion multiplied by 1 minus sample proportion divided by n...

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