**Black Raspberries and Cancer**Sample surveys usually contact large samples, allowing the use of large-sample confidence intervals if the sample design is close to a SRS (Simple Random Sample). However, scientific studies often use smaller samples that require the plus four method. For example, Familial Adenomatous Polyposis (FAP) is a rare inherited disease characterized by the development of an extreme number of polyps early in life, leading to colon cancer in virtually 100% of patients before age 40. A study involved 14 people suffering from FAP at the Cleveland Clinic, who drank black raspberry powder in a slurry daily for nine months. The number of polyps was reduced in 11 out of these 14 patients.**Questions:**(a) Why can’t we use the large-sample confidence interval for the proportion *p* of patients suffering from FAP that will have the number of polyps reduced after nine months of treatment?(b) The plus four method adds four observations—two successes and two failures. What are the sample size and the number of successes after doing this? What is the plus four estimate $\tilde{p}$ of *p*?(c) Provide the plus four 90% confidence interval for the proportion of patients suffering from FAP who will have the number of polyps reduced after nine months of treatment.

Given p=proportion of people whose polyps reduced after drinking black rasberry powder for 9 months =1114n=Sample size of the patients who have polyps and drank black rasberry powder for 9 months =14We cannot use a large sample confidence interval for the proportion p of patients suffering from FAP that will have the number of polyps reduced after 9 months of treatment because while calculating intervals with the four plus method , it is believed that the error term will be reduced which are introduced due to using estimates of population variance in order to calculate the standard deviation and the four plus method is believed to give confidence intervals more accurately when smaller samples are used rather than large samples. Thus large sample confidence intervals are not usedAfter the plus four method where two failures and successes were added the new N=New sample size after the add four method=18p^ =New proportion of patients whose plyps reduced after the add four mrthod =1318So the p^ to estimate p is 1318 Since the sample is binomial and since n×p is greater than 5 we can calculate the interval with the help of normal approximation where p^ ~N(0.1) At 90% confidence the confidence interval for p is =p^ ±Zα2 p^(1-p^)n=1318±1.644913181-1318N=(0.54857;0.89588) Therefore confidence interval for p is (0.54857;0.89588)

Math

Statistics

(a) Why can't we use the large-sample confidence interval for the propor- tion p of patients suffering from FAP that will have the number of polyps reduced after nine months of treatment? (b) The plus four method adds four observations-two successes and two failures. What are the sample size and the number of successes after you do this? What is the plus four estimate p of p? (c) Give the plus four 90% confidence interval for the proportion of patients suffering from FAP who will have the number of polyps reduced after nine months of treatment.

(a) Why can't we use the large-sample confidence interval for the propor- tion p of patients suffering from FAP that will have the number of polyps reduced after nine months of treatment? (b) The plus four method adds four observations-two successes and two failures. What are the sample size and the number of successes after you do this? What is the plus four estimate p of p? (c) Give the plus four 90% confidence interval for the proportion of patients suffering from FAP who will have the number of polyps reduced after nine months of treatment.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: Sample 1 Sample 2 "1 = 400 "2 n2 = 300 P₁ = 0.53 P₂ = 0.35 What is the point estimate of the…

A: For sample 1:sample size (n1)= 400sample proportion p1^ = 0.53For sample 2:sample size (n2)=…

Q: Nina would like to estimate the difference in the mean amount of time students spend on math…

A: Total number of sample =30 90% confidence interval for the true difference in the population means,…

Q: Pottery Archaeologists can use the chemical composi-tion of clay found in pottery artifacts to…

A: Obtain the 95% confidence interval for the difference in aluminum oxide content of pottery made at…

Q: Consider the following results for independent samples taken from two populations. Sample 1 Sample 2…

A: Given: n1=400n2=300 p1¯= 0.48p2¯= 0.32

Q: What is the chi-square value for the region to the right for a 999% confidence interval if the…

A: From the given information, the test is right-tailed, n=30

Q: A study of 420,059 cell phone users found that 135 of them developed cancer of the brain or nervous…

A: Do cell phone users appear to have a rate of cancer of the brain or nervous system that is different…

Q: Dr. Dream, an expert in infectious diseases, wanted to estimate the proportion of the adult…

Q: Find the margin of error at 94% confidence interval for n=347 and p = 0.42 Give your answer to three…

Q: You may need to use the appropriate appendix table or technology to answer this question. The…

A: Sample 1 Sample 2 n1 = 50 n2 = 25 x1 = 13.6 x2 = 11.6 X1 = 2.3 X2 = 3

Q: Find critical value (t- a/2 ) that corresponds to a confidence level of 90% and sample size n=12

A: We have to find out critical value...

Q: Working Breath Rate Two random samples of 32 individuals were selected. One sample participated in…

A: Given that : xˉ=14,σ=4.2,n=32α=1−C=1−0.9=0.10zc=z2a=z20.10=1.645(critical value is obtain from…

Q: A quality control analyst has collected a random sample of 12 batteries used in heart pacemakers and…

A: Step 1: The following are the requirements to construct 95% confidence interval estimate of the mean…

Q: Find the critical value Z a/2 for the 92% confidence interval.

A: We have given information, The confidence level is C=0.92. Here we have to obtain critical value of…

Q: ou collect a random sample of 66 webpage load times in milliseconds (ms) from the server logs. The…

A: Given data, n=66 x=397 s=33.7 Alpha=0.01 df=n-1=65 t-critical value is tc=2.653

Q: You may need to use the appropriate appendix table or technology to answer this question. Consider…

A: The 90% confidence interval for the difference in the two proportions is Interpretation: One can be…

Q: What is the sample size required to construct a 90% confidence interval for the population mean with…

A: Given,E=0.2z-value at 90% confidence is Zc=1.645Let the last two digits of your student ID is…

Q: Determine the P-value and decide whether at the 5% significance level, the data provide sufficient…

Q: Determine the value of the z* multiplier that would be used to compute an 75% confidence interval…

A: Determine the value of the Z* multiplier that would be used to compute an 75% confidence interval…

Q: You collect a random sample of 50 webpage load times in milliseconds (ms) from the server logs. The…

A: Given, n = 50 x¯ = 210 s = 33.6

Q: 95% confidence, develop an interval estimate for the difference between the average miles per gallon…

Q: A cellular phone company is interested in estimating the difference between the mean ages of females…

Q: If we have a sample of size 10 from a normal population with sample variance 16, what is the 99…

A: Given information- Sample size n = 10 Sample standard deviation s2 = 16 Confidence level = 0.99…

Q: Glaucoma is a leading cause of blindness in a certain country. An ophthalmologist measured the…

A: A confidence interval is a numeric value that a researcher will be reasonably confident in and…

Q: Using independent random samples, a researcher is comparing the number of hours of television viewed…

A: Given For the seniors of sample size 32, the mean is 3.9 hours with standard deviation of 1.2 hours.…

Q: Fed-Ex claims that the variance of their 2-day package delivery is less than 0.75 days. A simple…

Q: The pH of rain, measured at a weather station in Michigan, was observed for 39 consecutive rain…

Q: Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.t Suppose a small…

A: The known values are, Critical values: Using the z-table, the critical value at 80% confidence…

Q: A sample of marine iguanas (n=30) from the Galapagos Islands has an average length of 2.8ft with a…

A: given data n=30df=n-1=30-1=29x¯=2.8S2=0.43s=0.43=0.6557CI=0.95α=1-0.95=0.05

Q: The critical value (z -score) for an 84% confidence interval for a two tailed test is approximately…

A: From the given information, The confidence level is 84%. Significance level is 100%-84%=16%=0.16…

Q: Results from the National Health and Nutrition Examination Survey (NHANES) conducted thirty years…

Q: You've collected a sample of 14 concrete blocks and weighed them. You want to produce a 99%…

A: Given that there are 14 concrete blocks.Let n = sample size = 14Confidence level is 99%.Significance…

Q: Find the critical value zα/2 needed to construct a(n) 98.3% confidence interval.

A: Here, we need to construct a 98.3% confidence interval. It means, level of significance in the…

Q: You may need to use the appropriate appendix table or technology to answer this question. Consider…

A: n1 = 400 n2 = 300 p1 = 0.49 p2 = 0.32

Q: Two different simple random samples are drawn from two different populations. The first sample…

A: Given that : Two different simple random sample are drawn from two different populations. Let α =…

Concept explainers

Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.

Question

**Black Raspberries and Cancer**

Sample surveys usually contact large samples, allowing the use of large-sample confidence intervals if the sample design is close to a SRS (Simple Random Sample). However, scientific studies often use smaller samples that require the plus four method.

For example, Familial Adenomatous Polyposis (FAP) is a rare inherited disease characterized by the development of an extreme number of polyps early in life, leading to colon cancer in virtually 100% of patients before age 40. A study involved 14 people suffering from FAP at the Cleveland Clinic, who drank black raspberry powder in a slurry daily for nine months. The number of polyps was reduced in 11 out of these 14 patients.

**Questions:**

(a) Why can’t we use the large-sample confidence interval for the proportion *p* of patients suffering from FAP that will have the number of polyps reduced after nine months of treatment?

(b) The plus four method adds four observations—two successes and two failures. What are the sample size and the number of successes after doing this? What is the plus four estimate $\tilde{p}$ of *p*?

(c) Provide the plus four 90% confidence interval for the proportion of patients suffering from FAP who will have the number of polyps reduced after nine months of treatment.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2 Part a

Step 3 Part b

Step 4 Part c

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Types of Data and Their Measurement$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

We have developed a new drug used to reduce fever and want to test its efficacy. Ten ER patients who are running a fever agree to take the new drug instead of the traditional treatment. Their temperatures are taken before the drug is administered and 30 minutes after taking the drug. The results are recorded in the Excel file below. Use the data to construct and interpret a 99% confidence interval for the mean change in temperatures of patients after taking this drug using Excel. Be sure to include any explanation necessary along with a sentence that explains what the interval means. First Temp Second Temp 100.1 98.9 101.3 99.1 102.1 99.2 102.7 99 101.9 98.7 100.8 98.6 103.1 99.4 102.5 99.2 103.5 100.1 101.7 99.2
In a random sample of 392 people that were tested for the Norcovirus, it was found that 314 did not have the virus. A 97% confidence interval was constructed to estimate the proportion of the population that does not have the Norcovirus. This confidence interval came out to be (0.76,0.84).
If n=410 and p (p-hat) =0.55, find the margin of error at a 90% confidence level Give your answer to three decimals
A researcher has 56 pairs of participants who each experience two different experimental conditions. The mean for the first condition was is 34.27 and the mean for the second condition is 33.67. Assuming that tcv(N = 55, α = .05) = 2.004 and sMD = .65, what is the value of the 95% confidence interval?
A flu shot is administered during flu season. We look at the effect of the shot on individuals who received the shot versus those who did not. In a sample of 100 patients that received the flu shot, the average recovery time after being infected with the flu was 4 days with a standard deviation of 1 day. What is a 95% confidence interval for the population average recovery time? O (3.99.4.01) (3.80, 4.20)
A repeated measures study is done to measure the change in IQ test scores taken on Monday versus those taken on Friday. There were n=9 participants in the study. The mean difference was MD =-5 points and the standard error for the mean difference was SMD=0.51. Construct a 95% confidence interval to estimate the size of the population mean difference.
A company that manufactures baseball bats believes that its new bat will allow players to hit the ball 30 feet farther than its current model. The owner hires a professional baseball player known for hitting home runs to hit ten balls with each bat and he measures the distance each ball is hit to test the company's claim. The results of the batting experiment are shown in the following table. Construct a 90 % confidence interval for the true difference between the mean distance hit with the new model and the mean distance hit with the older model. Assume that the variances of the two populations are the same. Let Population 1 be the distances of balls hit with the new model baseball bat and Population 2 be the distances of balls hit with the old model. Round the endpoints of the interval to one decimal place, if necessary. Hitting Distance (in Feet) New Model Old Model 215 234 202 298 224 294 211 246 215 268 248 211 255 226 228 284 247 221 214 259
You may need to use the appropriate appendix table or technology to answer this question. The following results come from two independent random samples taken of two populations. Sample 1 Sample 2 n1 = 60 n2 = 25 x1 = 13.6 x2 = 11.6 ?1 = 2.4 ?2 = 3 (a) What is the point estimate of the difference between the two population means? (Use x1 − x2.) (b) Provide a 90% confidence interval for the difference between the two population means. (Use x1 − x2. Round your answers to two decimal places.) to (c) Provide a 95% confidence interval for the difference between the two population means. (Use x1 − x2. Round your answers to two decimal places.) to
For a random sample of 64 overweight men, the mean of the number of pounds that they were overweight was 30. The standard deviation of the population is 4.2 pounds. (a) Find the best point estimate for the average number of excess pounds for all overweight men. (b) Construct a 95% confidence interval of the mean of these pounds.
What value of z-alpha/2 is used in a 90% confidence interval for the population mean?
A company that manufactures baseball bats believes that its new bat will allow players to hit the ball 30 feet farther than its current model. The owner hires a professional baseball player known for hitting home runs to hit ten balls with each bat and he measures the distance each ball is hit to test the company's claim. The results of the batting experiment are shown in the following table. Construct a 90 % confidence interval for the true difference between the mean distance hit with the new model and the mean distance hit with the older model. Assume that the variances of the two populations are the same. Let Population 1 be the distances of balls hit with the new model baseball bat and Population 2 be the distances of balls hit with the old model. Round the endpoints of the interval to one decimal place, if necessary. Hitting Distance (in Feet) New Model 246 240 272 262 237 250 247 235 261 216 Old Model 293 232 299 279 239 228 256 292 272 298
The accompanying data represent the running times of files produced by two motion-picture companies. Assume that the running-time differences are approximately normally distributed. Construct a 90% confidence interval for 90% confidence interval for μ - μ were created, should it be assumed that o² = = If a Company | 106 96 105 Time (minutes) 91 99 II 101 78 123 89 171 89 120 Click here to view page 1 of the table of critical values of the F-distribution, for alpha = 0.05. Click here to view page 2 of the table of critical values of the F-distribution, for alpha = 0.05. The confidence interval is < (Round to three decimal places as needed.)