Question

Please write a 10 pages' statistical report how to study the length of sharks. You and use internet or other resources to obtain additional information. The basic information is given below Great white are big and hungry. Here are the lengths in feet of the following great whites: 18.7 12.3 18.6 15.7 18.3 14.6 15.8 14.9 17.6 12.1 16.4 16.7 17.8 16.2 12.6 17.8 13.8 12.2 15.2 14.7 12.4 13.2 15.8 14.3 16.6 9.4 18.2 13.2 13.6 15.3 16.1 13.5 19.1 16.2 22.8 16.8 13.6 15.3 16.1 13.5 19.1 16.2 22.8 16.8 13.6 13.2 15.7 19.7 18.7 13.2 16.8 Your report must include, but not limited to the following points. (a) Make a frequency distribution of the data set using eight classes. Include class limits, midpoints, boundaries, frequencies, relative frequencies, and cumulative frequencies. (b) Display the data using a frequency histogram and a frequency polygon orn the same axes. (c) Describe the distribution's shape as symmetric, uniform, or skewed. (d) Display the data using a stem-and-leaf plot. Use one line per stem (e) Display the data using an ogive. (f) Find the mean, median, and mode of the sample data set (g) Find the range, variance, and standard deviation of the data set (h) Find the coefficient of variation (i) 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 t procedures is safe with observations. 0) Display the data using a box-and-whisker plot. (k) Give a 95% confidence interval for the mean length of great white sharks Based on this interval, is there significant evidence at 5% level to reject the claim: Great white sharks average 20 feet in length? (1) It isn't clear exactly what parameter u you estimated in (k). What information do you need to say what u is?

need letters (i), (j), (k), and (l), please and thank you

Answer 1

Summary for Length of sharks Anderson-Darling Normality Test A-Squared P-Value 0.42 0.310 15.741 StDev Variance 7.052 Skewness 0.433013 0.635636 51 9.400 1st Quartile13.600 3rd Quartile 17.600 95% Confidence Interval for Mean 14.994 16.488 95% Confidence Interval for Median 14.700 16.400 95% Confidence Interval for StDev 95% Confidence Intervals 3.301 2.222 Median

(i) It is bell-shaped distribution. Center (mean)=15.741, Median=15.800, hence Mean is almost equal to median.

Lower Whisker=1st Quartile-1.5(3rd Quartile-1st Quartile)=13.6-1.5*(17.6-13.6)=7.6

Upper Whisker=3rd quartile+1.5(3rd Quartile-1st Quartile)=17.6+1.5*(17.6-13.6)=23.6

We know any value lies outside (7.6,23.6) is an outlier. Since here maximum and minimum values lie inside the interval so there is no outlier. The distribution is reasonably normal since p-value of AD test>0.05.

(k) 95% C.I. for mean length=(14.994, 16.488)

Since 20 is larger than upper limit of 95% C.I. for mean length so there is significant evidence at 5% level to reject the claim that great white sharks average 20 feet in length.

(l) We need point estimate of $\mu$ i.e. sample mean=15.741.