Question

In: Statistics and Probability

4-5. In the summer of 2003, The New England Journal of Medicine published results of some...

4-5. In the summer of 2003, The New England Journal of Medicine published results of some Scandinavian research. Men diagnosed with prostate cancer were randomly assigned to either undergo surgery or not. Among the 347 men who had surgery (group 1), 9 eventually died of prostate cancer compared with 31 of the 348 men (group 2) who did not have surgery. The researchers want to determine if surgery increases the chance of survival. Let p1: proportion of men that survived after surgery and p2: proportion of men that survived without surgery.

4. Construct a two-tailed 95% confidence interval for the difference between men’s survival without and with surgery and interpret it in terms of the problem context.

a. Justify assumptions for your CI.

b. Compute the 95% confidence interval and interpret it:

5. Apply a Hypothesis testing.

a. What are the null and alternative hypotheses?

b. Justify the assumptions before you compute your test statistic and then compute the test statistic.

c. What is the p-value for this test?

d. What would you conclude from this test at 5% level of significance?

Solutions

Expert Solution

4)

a)

Total number of sample 1 (n1) = 347

Total number of sample 2 (n2) = 348

number of favourable events (X1) = 9

number of favourable events (X2) = 31

Confidence interval(in %) = 95

z @ 95% = 1.96

b)

Since we know that

Required confidence interval = (-0.063-0.0343, -0.063+0.0343)

Required confidence interval = (-0.0973, -0.0287)

5)

Total number of sample 1 (n1) = 347

Total number of sample 2 (n2) = 348

number of favourable events (X1) = 9

number of favourable events (X2) = 31

a) We are interested in testing the hypothesis

b)

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

P = (0.0001768622861287863)

P = 0.0002

d)

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

Decision Rule: Reject the null hypothesis if the test statistic value is less than the critical value -1.6448536269514722 or greater than the critical value 1.6448536269514722

The statistic value, -3.5724 is less than the critical value -1.6448536269514722. Hence, reject the null hypothesis.

The researchers claim that surgery increases the chance of survival is true

Please hit thumps up if the answer helped you.


Related Solutions

In the summer of 2003, The New England Journal of Medicine published results of some Scandinavian...
In the summer of 2003, The New England Journal of Medicine published results of some Scandinavian research. Men diagnosed with prostate cancer were randomly assigned to either undergo surgery or not. Among the 347 men who had surgery (group 1), 16 eventually died of prostate cancer compared with 31 of the 348 men (group 2) who did not have surgery. The researchers want to determine if surgery increases the chance of survival. Let p1: proportion of men that survived after...
According to a study published in the New England Journal of Medicine, overweight people on low-carbohydrate...
According to a study published in the New England Journal of Medicine, overweight people on low-carbohydrate and Mediterranean diets lost more weight and got greater cardiovascular benefits than people on a conventional low-fat diet (The Boston Globe, July 17, 2008). A nutritionist wishes to verify these results and documents the weight loss (in pounds) of 30 dieters on the low-carbohydrate and Mediterranean diets and 30 dieters on the low-fat diet. Let Low-carb or Mediterranean and Low-fat diets represent populations 1...
An October 25, 2012 article in the New England Journal of Medicine reports the results of...
An October 25, 2012 article in the New England Journal of Medicine reports the results of a study examining aspirin and survival among patients with colorectal cancer. The following pieces of text are taken directly from the article abstract: (my edits are in italics) “METHODS We obtained data on 964 patients with rectal or colon cancer from the Nurses’ Health Study and the Health Professionals Follow-up Study, including data on aspirin use after diagnosis and the presence or absence of...
4. A study in New England Journal of Medicine wanted to estimate the proportion of all...
4. A study in New England Journal of Medicine wanted to estimate the proportion of all needle injection-drug users, who test HIV-positive in New Haven, Connecticut by selecting a sample. How large should the sample size be so that the confidence interval for proportion has a margin of error within ±5% of the population proportion with 99% confidence level if a preliminary sample found that 67.5% of needles used by injection-drug users are HIV-positive?
A survey of 192 medical school interns, whose results were published in the New England Journal...
A survey of 192 medical school interns, whose results were published in the New England Journal of Medicine in January 2005, found them to average 57 hours of work a week, with standard deviation of 16 hours. (a) Explain why the distribution of sample mean, x, will have an approximate normal shape even if the distribution of hours worked is not normal. The standard deviation is large. The sample size is small.      The standard deviation is small. The sample size...
An article in the New England Journal of Medicine reported that among adults living in the...
An article in the New England Journal of Medicine reported that among adults living in the US, the average level of albumin in cerbrospinal fluid is 29.5 mg/dl, with a standard deviation of 9.25 mg/dl. We are going to select a sample of size 20 from this population. a. How does the variability of our sample mean compare to the variability of albumin levels in the popoulation? b. What is the probability that our sample mean will be greater than...
An article in the New England Journal of Medicine described a randomized experiment that investigated the...
An article in the New England Journal of Medicine described a randomized experiment that investigated the effectiveness of two medications for nausea in patients undergoing chemotherapy treatments for cancer. In the experiment, 157 patients were divided at random into two groups. One group of 78 patients were given a standard anti-nausea drug called prochlorperazine, while the other group of 79 patients received delta-9-tetrahydrocannabinol (i.e., THC, the active ingredient in marijuana). Both medications were delivered orally and no patients were told...
Authors in the New England Journal of Medicine investigated a possible link between Zika virus and...
Authors in the New England Journal of Medicine investigated a possible link between Zika virus and microcephaly (or other fetus developmental abnormalities) and researchers collected the following data from Rio de Janeiro state in Brazil (data from March 2016): Baby with microcephaly Baby without microcephaly Row totals Pregnant mum with Zika 12 30 42 Pregnant mum w/o Zika 0 16 16 Column totals: 12 46 58 Test for independence between maternal Zika virus infection and a baby’s microcephaly. Report here...
A New England Journal of Medicine study (November 1986) found that a substantial portion of acute...
A New England Journal of Medicine study (November 1986) found that a substantial portion of acute hospital care is reported to be unnecessary. The physicians who conducted the study reviewed the medical records of 1,132 patients hospitalized at six different locations across the country. Overall, 60% of admissions in the sample were judged to be appropriate, 23% were deemed inappropriate, whereas 17% could have been avoided by the use of ambulatory surgery. Let p1, p2, and p3 represent the true...
5.2.5 ​Researchers Wilt et al. (New England Journal of Medicine, 2012) investigated whether surgery, compared to...
5.2.5 ​Researchers Wilt et al. (New England Journal of Medicine, 2012) investigated whether surgery, compared to just observation, was (more) effective in improving men’s survival chances after being diagnosed with prostate cancer. The researchers identified 731 men with localized prostate cancer who volunteered to participate. They randomly assigned 364 men to surgery and the remaining 367 to observation. All participants were followed for about 10 years. In those 10 years, 21 surgery recipients died of prostate cancer related reasons compared...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT