Problem

Biological effects of magnetic fields are a matter of current concern and research. In a...

Biological effects of magnetic fields are a matter of current concern and research. In an early study of the effects of a strong magnetic field on the development of mice (Barnothy 1964), 10 cages, each containing three 30-day-old albino female mice, were subjected for a period of 12 days to a field with an average strength of 80 Oe/cm. Thirty other mice housed in 10 similar cages were not placed in a magnetic field and served as controls. The following table shows the weight gains, in grams, for each of the cages.

a. Display the data graphically with parallel dotplots. (Draw two parallel number lines and put dots on one corresponding to the weight gains of the controls and on the other at points corresponding to the gains of the treatment group.)

b. Find a 95% confidence interval for the difference of the mean weight gains.

c. Use a t test to assess the statistical significance of the observed difference. What is the p-value of the test?

d. Repeat using a nonparametric test.

e. What is the difference of the median weight gains?

f. Use the bootstrap to estimate the standard error of the difference of median weight gains.

g. Form a confidence interval for the difference of median weight gains based on the bootstrap approximation to the sampling distribution.

Step-by-Step Solution

Solution 1

Step #1 of 9

(a)

The Graphical display of control and treated group is given in the below figure.

The graph represents the dots on one corresponding to the weight gains of the controls and on the other at points corresponding to the gains of treatments group.

Step #2 of 9

(b)

Using Minitab, the 95 % confidence interval for difference or means is as shown below:

By using Minitab software to test the difference between two means, we need the following instructions.

1. Click Stat, Basic Statistics, and 2-Sample t…

2. Click Samples in different column, enter Field present in First, and enter Field absent in second.

3. Click on Assume equal variances.

4. Click Options…, you must specify the Alternative hypothesis as not equal to conduct a two-tailed test.

5. Click OK.

Step #3 of 9

Follow the instructions to get the required results as shown below:

From the output, obsreve that the 95% confidence interval is, (-12.09,-3.45).

Step #4 of 9

(c)

Using Minitab, perform a t-test to assess the statistical significance test is as follows.

From the above Minitab, the t-statistic . The p-value to the correspondind test statiatic is 0.001. Since the p-value of the test is less than reject our claim. It conclude that there is a statistically significant between the treated and control group.

Step #5 of 9

(d)

Using Minitab, to perform Mann-Whitny test under the following instructions.

Now compute the required test statistic using MINITAB by following the instructions:

1. Type or import the data into two columns.

2. Click Stat, Nonparametric, and Mann-Whitney….

3. Type the variable name for the First Sample, the variable name for the Second Sample, and click one of less than, not equal to, or greater than in the Alternative box.

4. Then click OK.

Step #6 of 9

Follow the instructions to get the required results as shown below:

From the above Minitab, the test-statistic The p-value of the test is, 0.0046. Since the p-value of the test is less than reject our claim. It conclude that there is a statistically significant between the treated and control group.