Question

Question 2 Hodgkin disease is a malignant condition characterised by enlarged lymph nodes, spleen and general lymphoid tissues. Patients suffering from this condition will require some form of radiation therapy to manage the symptoms. A new form of chemotherapy has been developed which claims to not have as many side effects as the traditional methods of chemo. The table provided summarises the measurements of the before and after biopsies for a sample of 10 patients suffering from Hodgkin lymphoma. We are interested in knowing if this new form of chemo affects the size of patient's l ymphoid tissues Diagnosis Hodgkin's Lymphoma Prior to 3.52 1.93 After treatment 3.30 2.08 Difference 0.22 0.56 treatment Mean (lymphoid size Std. Deviation a. State the null and alternative hypotheses for this scenario. (2 marks) b. Using the critical value method, obtain a test statistic for this scenario (use a 0.01). (4 marks) c. An analysis of this data set was conducted using SPSS. Using the generated output, what is to correct decision to make regardin g Ho? (2 marks) Paired Differences Mean Std Deviation Std. Error Mean Sig. (2-tailed) df Pair Prior - 22000 56000 177001.243 337 After d. Using your solutions to Questions b. and/or c., state your conclusion for this scenario. (2 marks)

Please have neat hand writing.

Answer 1

From the sample data, it is found that the corresponding sample means are:

Also, the provided sample standard deviations are:

$\\s_1 = 1.93\\s_2 =2.08$

and the sample size is n = 10. For the score differences we have

$\\\bar D = 0.22\\ s_D = 0.56$

(3) Test Statistics

The t-statistic is computed as shown in the following formula:

$\\\bar D = 0.22\\ s_D = 0.56 t = \frac{\bar D}{s_D/ \sqrt n} \\ = \frac{0.22}{0.56/ \sqrt{10}} \\ \\=1.242323$

(4) The decision about the null hypothesis

Since it is observed that $|t| = 1.2423 \le t_c = 3.25$ it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p = 0.24552, and since $p = 0.24552 \ge 0.01$ it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ1 is different than μ2, at the 0.01 significance level.

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