Question

As part of a study of the development of the thymus gland, researchers weighted the glands of 51 chick embryos after 14 days of incubation. The mean thymus weight is 30.7 and the standard deviation is 8.4 (c). (1 pt) Is 99% CI wider than 95% CI (You do not need to calculate the 95% CI)?

Answer 1

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Answer:

Without calculation we can say that  a 99% confidence interval will be wider than a 95% confidence interval because to be more confident that the true population value falls within the interval we will need to allow more potential values within the interval

The computation for 95% confidence interval is

mean +- zcritical*standard error (zcrit = 1.96)

=> 30.8 +- 1.96*8.4/sqrt(51) ( Since Standard error = Standard deviation/sqrt(numbers of data)

= 30.8 +- 2.305

= 28.495, 33.105

The computation for 99% confidence interval is

mean +- zcritical*standarde error (zcrit = 2.58)

30.8 +- 2.58*8.4/sqrt(51)

= 30.8 +- 3.035

= 27.765, 33.835

From this we can clearly see that only zcrit varies in the formula for 99% as it accomodates larger range than for the range in 95% confidence interval