Question

Great white sharks are big and hungry. Here are the lengths in feet of 44 great whites.

18.6 16.3 13.3 19.0

12.5 16.5 15.7 16.4

18.5 17.8 14.1 23.0

16.6 16.1 16.8 16.6

15.6 12.7 9.3 13.7

18.4 18.0 18.3 13.4

14.4 13.7 13.3 15.8

15.7 12.1 13.7 19.5

14.8 15.3 15.4 18.6

17.6 14.8 15.9 13.2

12.1 12.5 13.4 16.9

(a) Examine these data for shape, center, spread and outliers. The distribution is reasonably Normal except for one outlier in each direction. Because these are not extreme and preserve the symmetry of the distribution, use of the tprocedures is safe with 44 observations. (Round your answer for x to two decimal places and your answer for s to three decimal places.)

x	=  ft
s	=  ft

(b) Give a 95% confidence interval for the mean length of great white sharks. (Round your answers to two decimal places.)
to  ft

Based on this interval, is there significant evidence at the 5% level to reject the claim "Great white sharks average 20 feet in length"?

Since 20 ft does not fall in this interval, we reject this claim.Since 20 ft does not fall in this interval, we accept this claim.    Since 20 ft does fall in this interval, we accept this claim.Since 20 ft does fall in this interval, we reject this claim.

(c) Before accepting the conclusions of (b), you need more information about the data. What would you like to know? (Select all that apply.)

Were they all male?Were these all full-grown sharks?Are these sharks dangerous?Were these all great white sharks?Had these sharks just eaten?Can these numbers be considered an SRS from this population?

Answer 1

a) From the given data, first we draw box plot

There is one outlier appeared in the box plot. First we remove the outlier. i.e. 12th observation is 23 is removed

The modifed box plot is

There is no outlier in the box plot

Normality Test:

The shape of the histogram is bell shaped and the points in Normal quanitity plot are near to straight line so the given data follows Normal distribution

From the given data

b)

The 95% confdience interval is (15.589 +/- 2.0181 * 2.303/sqrt(43)) =(14.8802, 16.2977)

correct answer: Option (A) Since 20 ft does not fall in this interval, we reject this claim.

c) Yes, these numbers be considered an SRS from this population