Question

Breast cancer specialists use BI-RADS scores (a whole number from 1 to 6) to classify mammogram findings. A score of 1 indicates a negative finding, while 6 indicates clear malignancy. The data set mammography.csv contains observations on 953 women who had mammograms and subsequent biopsies. For each woman, we have a BI-RADS score and the result of her biopsy (benign or malignant). Of interest is whether mean BIRADS score is, in fact, higher for women who have malignancies.

a. Which assumption is required to make inference about mean BI-RADS scores for women with and without malignancies?

b. What are the null and alternative hypotheses?

c. (1 mark) What is the value of the test statistic?

d. (1 mark) What is the approximate p-value?

e. Which assumption is required for the p-value in c) to be valid?

f. Using a significance level of = 0.05, state your conclusions in the language of the problem.

file=

"BI.RADS","Diagnosis"

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Answer 1

	Benign	Malignnant
n	513	440
Mean	3.981	4.711
Std	0.511	0.532

a) Sample size is more than 30 and assumed to be approximatley normal. Variance between two variables is equal or not.

b) Two sample t test with equal variances:

c) The test statistic:

pooled variance:

d) The degree of freedom= n1+n2-2= 951

P-value: 0.000

e) The test statistic is significant and rejects H0.

f) There is sufficient evidence to support the claim that the mean BIRADS score is higher for women who have malignancies.