5. Lung Cancer is the leading cause of cancer deaths in both women and men in the US. According to the Center for Disease Control and Prevention, lung cancer accounted for more deaths than breast cancer, colon cancer, and prostate cancer combined. Overall, only about 19.4% of people who develop lung cancer survive for 5 years. a. Use this information (and a provisional initial value of p of 0.194) to determine the sample size needed for a 95% confidence interval of the true proportion surviving for five years after diagnosis to within 1%. That is, the planned margin of error E = 0.01.
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The problem asks us to calculate the sample size needed to estimate the true proportion of lung cancer patients who survive for 5 years, with a 95% confidence level and a margin of error of 1% (or 0.01 in decimal form). The initial estimate of the proportion (p) Show more…
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Lung cancer is the leading cause of cancer deaths in both women and men in the United States. According to Centers for Disease Control and Prevention 2005 statistics, lung cancer accounts for more deaths than breast cancer, prostate cancer, and colon cancer combined. Overall, only about $16 \%$ of all people who develop lung cancer survive 5 years. Suppose you want to see if this survival rate is still true. How large a sample would you need to take to estimate the true proportion surviving 5 years after diagnosis to within $1 \%$ with $95 \%$ confidence? (Use the $16 \%$ as the initial value of $p .$ )
Inferences Involving One Population
Inferences about the Binomial Probability of Success
Q6. Of 1000 randomly selected cases of lung cancer, 823 resulted in death within 10 years. (a) Calculate a 95% two-sided confidence interval on the death rate from lung cancer. (b) Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.03? (c) How large must the sample be if you wish to be at least 95% confident that the error in estimating p is less than 0.03, regardless of the true value of p?
Kari H.
Suppose two independent random samples were taken. The following data were recorded: Quebec: ð‘›1 = 150, Number of deaths due to cancer = ð‘¥1 = 47 Rest of Canada: ð‘›2 = 1000, Number of deaths due to cancer = ð‘¥2 = 291 (Round your answers to 3 decimal places) (a) Test the appropriate hypothesis to determine whether the data provide sufficient evidence to indicate a difference between the two population proportion parameters. Use α = 0.01 and the critical value approach. (b) Find the p-value for the test and write your conclusion at the 1% significance level. (c) Use a 99% confidence interval to estimate the actual difference between the cancer death proportions for the people in Quebec versus the rest of Canada. Does your confidence interval estimate provide the same conclusion as in part (a)? Justify your answer.
Sri K.
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