Question

One study on the effects of cannabis used rats as test organisms; data in the table below describe the weight (g) of livers harvested from some of the test rats.

13.47, 12.19, 6.35, 12.62, 6.8, 6.78, 6.62, 10.3, 10.21, 8.47, 5.56, 9.83

7.62, 4, 9.82, 5.2, 8.61, 11.7, 9.76, 12.16, 7.87, 7.16, 12.31, 16.9, 6.72 Use these data to answer the following questions.

a) Fill in the missing sample statistics in the table; enter values to three decimal places.

Sample size Minimum Maximum Mean

Estimated standard deviation Estimated variance Estimated skewness Estimated kurtosis

b) Create a boxplot of the data, and include that figure as part of your solution. How many outliers do you think there are in this dataset?

c) Create a histogram of the data, and include that figure as part of your solution. What parametric distribution do you think is appropriate for the data?

d) Create a quantile‐quantile plot of the data showing the sample quantiles as a function of the theoretical quantiles of a normal distribution. Include a theoretical ideal fit reference line. Include that figure as part of your solution. Do the data appear to fit a normal distribution?

Assume you elected to model the data using a normal distribution:

e) What parameter values would you recommend for that model?

f) What are the estimated standard errors of those parameters?

The following questions are based on the assumption that a normal distribution is an appropriate model.

g) What are the lower and upper limits of an 85% confidence interval on the mean?

h) What are the lower and upper limits of an 85% confidence interval on the standard deviation?

i) What are the lower and upper limits of an 85% confidence interval on a prediction for the next

sample drawn?

Answer 1

Solution:

a) I have used excel the calculate the missing sample statistics.

Sample Statistics
Sample size	25
Minimum	4
Maximum	16.900
Mean	9.161
Standard Deviation	3.057
Sample Variance	9.345
Kurtosis	0.100
Skewness	0.555

b) The boxplot for the dataset is given below.

From the boxplot we can observe that there are no points outside the box. Hence, there are no outliers.

c) The histogram of the given data set is as follows.