Chapter 10: Q. 10.82 (page 428)

Phyllodes Tumors. Phyllodes tumors of the breast are rare tumors that represent less than one percent of growths in the breast. Researchers I. Youn et al. presented characteristics of phyllodes tumors in the article "Phyllodes Tumors of the Breast: Ultrasonographic Findings and Diagnostic Performance of Ultrasound-Guided Core Needle Biopsy" . The following table provides summary statistics for the sizes, in millimeters (mm), of independent samples of benign and malignant phyllodes tumors.
At the $1 %$ significance level, do the data provide sufficient evidence to conclude that, on average, malignant phyllodes tumors are larger than benign phyllodes tumors?

Short Answer

Expert verified

As a result, even at a $1 %$ level of significance, the data give enough evidence to conclude that the two population means are not comparable. The findings give sufficient evidence to indicate that malignant phyllodes tumours are larger on average than benign phyllodes tumours at the $1 %$ significance level.

Step by step solution

Given Information

Using the critical value approach or the value approach, determine the required hypothesis.

Explanation

The hypothesis test to be carried out is as follows:

$H_{a} : μ_{1} > μ_{2}$

The test is carried out at a significance level of localid="1651292246796" $a = 0.01$ , orlocalid="1651292251253" $1 %$

The test statistic's value is calculated as follows:

$t = \frac{{\bar{x}}_{1} - {\bar{x}}_{2}}{\sqrt{(\frac{s_{1}^{2}}{n_{1}}) + (\frac{s_{2}^{2}}{n_{1}})}}$

$= \frac{48.5 - 33.7}{\sqrt{(\frac{38.52}{52}) + (\frac{26.62}{116})}}$

The $t$ statistic has $d f = Δ$ .

Explanation

The probability of seeing a value $t = 2.52$ is given by the $P$ value. The value of $P$ obtained using technological means is $0.007$ . The significance level of $1 %$ is not exceeded by the $p$ value. As a result, the results are statistically significant at the $1 %$ level.