![\"Image](\"https:\/\/textbooks.jaykesler.net\/introstats\/wp-content\/uploads\/sites\/2\/2023\/08\/matt-palmer-kbTp7dBzHyY-unsplash-1024x683.jpg\")
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Figure <\/span>7.1<\/span> Fires burning on the Hawaiian islands in 2023.<\/span><\/div>\r\n<\/div>\r\n
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\r\n\r\nChapter Objectives<\/span><\/h3>\r\n<\/header>
Chapter Objectives<\/span><\/h3>\r\n<\/header>\r\n\r\nBy the end of this chapter, the student should be able to:<\/p>\r\n\r\n
\r\n \t- Distinguish between independent and paired\/dependent samples<\/li>\r\n \t
- Construct confidence intervals for the difference between two population means or proportions<\/li>\r\n \t
- Describe the pooled standard deviation and the known standard deviation methods<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/section><\/div>\r\nWe have already seen the usefulness of Confidence Intervals when we are trying to estimate a population parameter (mean or proportion). Often times we want to compare a parameter from two different populations. To do this, we can create a confidence interval to estimate the difference<\/span> between the two parameters.\r\n\r\n<\/div>\r\n<\/div>\r\nFor example, medical researchers may want to know whether a new treatment for colon cancer is effective. They can assign a group of patients to receive the new treatment and another group of patients to receive the old treatment. The researchers might then look at the difference in the proportion<\/em> of patients in each group who went into remission.<\/div>\r\nAs another example, the data below lists the sea surface high temperature recorded each month of the years 1960 and 2020.<\/div>\r\n\r\n
\r\n\r\n\r\n<\/td>\r\n 2020<\/span><\/strong><\/td>\r\n1960<\/span><\/strong><\/td>\r\n<\/tr>\r\n\r\nJanuary<\/strong><\/td>\r\n0.672<\/span><\/td>\r\n -0.016<\/span><\/td>\r\n<\/tr>\r\n\r\nFebruary<\/strong><\/td>\r\n0.6215<\/span><\/td>\r\n -0.0385<\/span><\/td>\r\n<\/tr>\r\n\r\nMarch<\/strong><\/td>\r\n0.6505<\/span><\/td>\r\n -0.0055<\/span><\/td>\r\n<\/tr>\r\n\r\nApril<\/strong><\/td>\r\n0.6475<\/span><\/td>\r\n -0.0315<\/span><\/td>\r\n<\/tr>\r\n\r\nMay<\/strong><\/td>\r\n0.671<\/span><\/td>\r\n 0.022<\/span><\/td>\r\n<\/tr>\r\n\r\nJune<\/strong><\/td>\r\n0.737<\/span><\/td>\r\n -0.037<\/span><\/td>\r\n<\/tr>\r\n\r\nJuly<\/strong><\/td>\r\n0.718<\/span><\/td>\r\n 0.061<\/span><\/td>\r\n<\/tr>\r\n\r\nAugust<\/strong><\/td>\r\n0.776<\/span><\/td>\r\n 0.05<\/span><\/td>\r\n<\/tr>\r\n\r\nSeptember<\/strong><\/td>\r\n0.726<\/span><\/td>\r\n 0.0785<\/span><\/td>\r\n<\/tr>\r\n\r\nOctober<\/strong><\/td>\r\n0.705<\/span><\/td>\r\n -0.0245<\/span><\/td>\r\n<\/tr>\r\n\r\nNovember<\/strong><\/td>\r\n0.6875<\/span><\/td>\r\n -0.0195<\/span><\/td>\r\n<\/tr>\r\n\r\nDecember<\/strong><\/td>\r\n0.7415<\/span><\/td>\r\n 0.016<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
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By the end of this chapter, the student should be able to:<\/p>\r\n\r\n
- \r\n \t
- Distinguish between independent and paired\/dependent samples<\/li>\r\n \t
- Construct confidence intervals for the difference between two population means or proportions<\/li>\r\n \t
- Describe the pooled standard deviation and the known standard deviation methods<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/section><\/div>\r\nWe have already seen the usefulness of Confidence Intervals when we are trying to estimate a population parameter (mean or proportion). Often times we want to compare a parameter from two different populations. To do this, we can create a confidence interval to estimate the difference<\/span> between the two parameters.\r\n\r\n<\/div>\r\n<\/div>\r\nFor example, medical researchers may want to know whether a new treatment for colon cancer is effective. They can assign a group of patients to receive the new treatment and another group of patients to receive the old treatment. The researchers might then look at the difference in the proportion<\/em> of patients in each group who went into remission.<\/div>\r\nAs another example, the data below lists the sea surface high temperature recorded each month of the years 1960 and 2020.<\/div>\r\n\r\n
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\r\n <\/td>\r\n 2020<\/span><\/strong><\/td>\r\n 1960<\/span><\/strong><\/td>\r\n<\/tr>\r\n \r\n January<\/strong><\/td>\r\n 0.672<\/span><\/td>\r\n -0.016<\/span><\/td>\r\n<\/tr>\r\n \r\n February<\/strong><\/td>\r\n 0.6215<\/span><\/td>\r\n -0.0385<\/span><\/td>\r\n<\/tr>\r\n \r\n March<\/strong><\/td>\r\n 0.6505<\/span><\/td>\r\n -0.0055<\/span><\/td>\r\n<\/tr>\r\n \r\n April<\/strong><\/td>\r\n 0.6475<\/span><\/td>\r\n -0.0315<\/span><\/td>\r\n<\/tr>\r\n \r\n May<\/strong><\/td>\r\n 0.671<\/span><\/td>\r\n 0.022<\/span><\/td>\r\n<\/tr>\r\n \r\n June<\/strong><\/td>\r\n 0.737<\/span><\/td>\r\n -0.037<\/span><\/td>\r\n<\/tr>\r\n \r\n July<\/strong><\/td>\r\n 0.718<\/span><\/td>\r\n 0.061<\/span><\/td>\r\n<\/tr>\r\n \r\n August<\/strong><\/td>\r\n 0.776<\/span><\/td>\r\n 0.05<\/span><\/td>\r\n<\/tr>\r\n \r\n September<\/strong><\/td>\r\n 0.726<\/span><\/td>\r\n 0.0785<\/span><\/td>\r\n<\/tr>\r\n \r\n October<\/strong><\/td>\r\n 0.705<\/span><\/td>\r\n -0.0245<\/span><\/td>\r\n<\/tr>\r\n \r\n November<\/strong><\/td>\r\n 0.6875<\/span><\/td>\r\n -0.0195<\/span><\/td>\r\n<\/tr>\r\n \r\n December<\/strong><\/td>\r\n 0.7415<\/span><\/td>\r\n 0.016<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n