The Australian dragon fly, the world\'s fastest insect, has been clocked at 36 m

Question

The Australian dragon fly, the world's fastest insect, has been clocked at 36 miles per hour over short distances. A biologist captured 25 Australian dragon flies and she recorded the average wingspan of these captured dragon flies of 6.6cm. The biologist assumed that the wingspan is normally distributed with a standard deviation of 0.5cm.

a. Find a 98.3% confidence interval for the true mean wingspan for all dragon flies.

b. Interpret the interval obtained in part (a) in the context of this question.

c. If a 90% confidence interval for the true mean wingspan for all dragon flies is calculated, do you expect this interval be wider or narrower than the interval obtained in part (a)? Why?

d. If the biologist assumed that the standard deviation of the wingspan of Australia dragon fly is 0.25cm and a 98.3% confidence interval for the true mean wingspan for all dragon flies is calculated, do you expect this interval be wider or narrower than the interval obtained in part (a)? Why

Explanation / Answer

1) For a 95% confidence interval , z = 2.38 from normal distribution tables.

Hence, Confidence interval is 6.6+- (2.38*0.5) = (5.41,7.79)

2) There is a 98.3% chance that the wingspan of a Australian dragnonfly will lie between 5.41 and 7.79 cm

3)It will be narrower as z-value for 90% is smaller than z value for 98.3%. Confidence interval = 2 * z value * standard error.

4) Interval will be narrower since standard deviation and standard error would be lower. Confidence interval = 2* z value * standard error.

Standard error is a funtion of standard deviation.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.