Question

In: Statistics and Probability

A method currently used by doctors to screen women for possible breast cancer fails to detect...

A method currently used by doctors to screen women for possible breast cancer fails to detect cancer in 20% of the women who actually have the disease. A new method has been developed that researchers hope will be able to detect cancer more accurately. A random sample of 81 women known to have breast cancer were screened using the new method. Of these, the new method failed to detect cancer in 14. Let p be the true proportion of women for which the new method fails to detect cancer. The investigator wants to conduct an appropriate test to see if the new method is more accurate using α = 0.05. Assume that the sample size is large.

Answer the following four parts

Part 1) What is the research hypothesis?

(a)Ha : p ≠ 0.20

(b)Ha : p > 0.20

(c)Ha : p < 14/81

(d)Ha : p < 0.20

Part 2) Report the value of the appropriate test statistic formula.

Part 3) What is the approximate p-value of your test?

(a)0.7291

(b)0.2291

(c)0.2709

(d)0.39

Part 4) What is the conclusion?

(a) Suﬃcient evidence to say that the new method is more accurate than the method currently used by the doctors

(b) Insuﬃcient evidence to say that the new method is more accurate than the method currently used by the doctors

(c) Reject H0 at α = 0.05

Expert Solution

Total number of sample (n) = 81

number of favourable events (X) = 14

1)

We are interested in testing the hypothesis

2)

3)

Since P-value of a two tailed test is equal to

P = (0.27086668991567534)

P = 0.2709

4)

Here, the P-value is greater than the level of significance 0.05; Fail to reject the null hypothesis

Decision Rule: Reject the null hypothesis if the test statistic value is less than the critical value -1.64 or greater than the critical value 1.64

The statistic value, -0.6111 is greater than the critical values -1.64. Therefore, we fail to reject the null hypothesis.

We have suﬃcient evidence to say that the new method is more accurate than the method currently used by the doctors

Please hit thumbs up if the answer helped you.

orchestra answered 1 year ago

A mammogram was used to screen for breast cancer in 200 women with breast cancer diagnosed...

A mammogram was used to screen for breast cancer in 200 women with breast cancer diagnosed by a biopsy and in 500 age- and race-matched women without breast cancer. The results of the mammogram were positive in 150 of the women with breast cancer and in 100 of the women without breast cancer. b. Compute the i) sensitivity, ii) specificity, iii) positive predictive value, and iv) negative predictive value. c. Make a statement about each of the computations d. If...

Given these facts: Using the case of testing women for breast cancer (*) 1% have breast...

Given these facts: Using the case of testing women for breast cancer (*) 1% have breast cancer 99% don’t have breast cancer Mammogram tests In event of a woman with cancer 80% of mammograms detect breast cancer when it is there (positive) 20% miss it (false negative) In event of no cancer 9.6% of mammograms detect breast cancer when it’s not there (false positive) 90.4% correctly return a negative result. Questions: A lady takes the test three times and all...

16. An epidemiologic study of breast cancer among elderly women followed 1,000 women, 65-79 years of...

16. An epidemiologic study of breast cancer among elderly women followed 1,000 women, 65-79 years of age, without evidence of breast cancer over several years. Every two years the investigators examined the women for breast cancer. The results were as follows: 12 new cases at the first evaluation, 11 new cases at the second evaluation, 23 new cases at the third evaluation, and 28 new cases at the fourth (and final) evaluation. The investigators also noted that 40 women had...

Patients with breast cancer sometimes die for other reasons. In a Nurses’ Health study, women with...

Patients with breast cancer sometimes die for other reasons. In a Nurses’ Health study, women with breast cancer were followed for 10 years and 2.5% had incidence of heart disease. Suppose the baseline 10-year incidence rate of heart disease in the general population is 2%. Assume a study is to be undertaken tracking women with breast cancer to see if there is a difference in the heart disease rate from the general population. Assuming the true heart disease incidence rate...

Epidemiologists claim that the probability of breast cancer among Caucasian women in their mid-60s is 0.003....

Epidemiologists claim that the probability of breast cancer among Caucasian women in their mid-60s is 0.003. An established test identified people who had breast cancer and those that were healthy. A new mammography test in clinical trials has a probability of 0.90 for detecting cancer correctly. In women without breast cancer, it has a chance of 0.975 for a negative result. If a 65-year-old Caucasian woman tests positive for breast cancer, what is the probability that she, in fact, has...

Exercise 1: Thirty nine women with a diagnosis of inoperable or metastatic breast cancer have been...

Exercise 1: Thirty nine women with a diagnosis of inoperable or metastatic breast cancer have been followed-up for a number of years, while under continuous treatment with a medication called trastzuzumab. The time (in months) each patient remained in remission was recorded. Remission is is a decrease or disappearance of signs and symptoms of cancer. Below is the data. 50 74 35 39 21 37 27 35 30 35 26 38 34 34 26 41 61 33 33 26 25...

thirty-nine women with a diagnosis of inoperable or metastatic breast cancer have been followed-up for a...

thirty-nine women with a diagnosis of inoperable or metastatic breast cancer have been followed-up for a number of years, while under continuous treatment with a medication called trastuzumab. the time (in months) each patient remained in remission was recorded. Remission is a decrease or disappearance of signs and symptoms of cancer. Below is the data. 50 74 35 39 21 37 27 35 30 35 26 38 34 34 26 41 61 33 33 26 25 41 35 34 44...

Epidemiologists decided to investigate the validity of new diagnostic tool for breast cancer. They used this...

Epidemiologists decided to investigate the validity of new diagnostic tool for breast cancer. They used this new diagnostic tool for breast cancer in 150 women with biopsy-proven breast cancer in 300 age- and race-matched control women. The results of the new tool were positive in 136 cases and in 35 control women, all of whom showed no evidence of cancer at biopsy. What is the sensitivity of new diagnosis tool for breast cancer? a. 33% b. 91% c. 9% d....

Literature shows that the incidence of breast cancer is 150 cases per 100,000 women aged 45-49...

Literature shows that the incidence of breast cancer is 150 cases per 100,000 women aged 45-49 years old annually. The researchers want to test whether regular intake of vitamin D would reduce 20% of the risk of the occurence of breast cancer. They plan to recruit women aged 45-49 years who are free of breast cancer at the beginning and randomly assign them into two groups, i.e., group one: women in this group will receive vitamin D treatment, and group...

Research Methond Suppose that among 100,000 women with negative mammograms, 20 will have Breast Cancer (BC)...

Research Methond Suppose that among 100,000 women with negative mammograms, 20 will have Breast Cancer (BC) diagnosed within 2 years; and among 100 women with positive mammograms, 10 will have BC diagnosed within 2 years. a. What is the Relative Risk (RR)? b. What is the Risk Difference (RD)? c. Restate your conclusion(s) in the form of a sentence.