Question

In: Statistics and Probability

Phyllodes tumors of the breast are rare tumors that represent less than one percent of growths...

Phyllodes tumors of the breast are rare tumors that represent less than one percent of growths in the breast. Some researchers presented characteristics of phyllodes tumors in an article. The following table provides summary statistics for the sizes, in millimeters (mm) of independent samples of benign and malignant phyllodes tumors. Suppose that these tumor sizes are normally distributed.

Use the nonpooled ?-test to answer the following: 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? (Note: Δ = 38)

Malignant

?1 = 48.5 ?1 = 38.5 ?1 = 23

Benign

?2 = 33.7 ?2 = 26.6 ?2 = 27

a. Hypotheses: ?0: _______________________ ??: __________________________

b. Compute the test statistic:

c. Determine the ?-value.

d. Reject null?

e. Step 6: Interpret your result in a sentence.

Thank You! I hope you're staying safe in this crazy time.

Solutions

Expert Solution

Part a)

H0 :- µ1 = µ2
H1 :- µ1 > µ2

Part b)

Test Statistic :-


t = 1.5544

Part c)

P - value = P ( t > 1.5544 ) = 0.0642 ( From t table )

Part d)

Decision based on P value
P - value = P ( t > 1.5544 ) = 0.0642
Reject null hypothesis if P value < α level of significance
P - value = 0.0642 > 0.01 ,hence we fail to reject null hypothesis
Conclusion :- Fail to Reject Null Hypothesis

d. Reject null? NO.

Part e)

There is insufficient evidence to support the claim that on average, malignant phyllodes tumors are larger than benign phyllodes tumors at 1% level of significance.

orchestra answered 2 years ago
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