{"id":1981,"date":"2022-01-26T20:01:29","date_gmt":"2022-01-26T20:01:29","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=1981"},"modified":"2022-02-09T01:12:35","modified_gmt":"2022-02-09T01:12:35","slug":"13c","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/13c\/","title":{"raw":"13C","rendered":"13C"},"content":{"raw":"<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>State<\/strong><\/td>\r\n<td><strong>Average Daily Screen Time <\/strong>\r\n\r\n<strong>(in minutes)<\/strong><\/td>\r\n<td><strong>\u00a0<\/strong><\/td>\r\n<td><strong>State<\/strong><\/td>\r\n<td><strong>Average Daily Screen Time (in minutes)<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Alabama<\/td>\r\n<td>170<\/td>\r\n<td><\/td>\r\n<td>Montana<\/td>\r\n<td>154<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Alaska<\/td>\r\n<td>134<\/td>\r\n<td><\/td>\r\n<td>Nebraska<\/td>\r\n<td>182<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Arizona<\/td>\r\n<td>276<\/td>\r\n<td><\/td>\r\n<td>Nevada<\/td>\r\n<td>262<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Arkansas<\/td>\r\n<td>145<\/td>\r\n<td><\/td>\r\n<td>New Hampshire<\/td>\r\n<td>135<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>California<\/td>\r\n<td>204<\/td>\r\n<td><\/td>\r\n<td>New Jersey<\/td>\r\n<td>182<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Colorado<\/td>\r\n<td>166<\/td>\r\n<td><\/td>\r\n<td>New Mexico<\/td>\r\n<td>177<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Connecticut<\/td>\r\n<td>262<\/td>\r\n<td><\/td>\r\n<td>New York<\/td>\r\n<td>206<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Delaware<\/td>\r\n<td>166<\/td>\r\n<td><\/td>\r\n<td>North Carolina<\/td>\r\n<td>205<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Florida<\/td>\r\n<td>213<\/td>\r\n<td><\/td>\r\n<td>North Dakota<\/td>\r\n<td>192<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Georgia<\/td>\r\n<td>198<\/td>\r\n<td><\/td>\r\n<td>Ohio<\/td>\r\n<td>231<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Hawaii<\/td>\r\n<td>133<\/td>\r\n<td><\/td>\r\n<td>Oklahoma<\/td>\r\n<td>131<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Idaho<\/td>\r\n<td>161<\/td>\r\n<td><\/td>\r\n<td>Oregon<\/td>\r\n<td>132<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Illinois<\/td>\r\n<td>220<\/td>\r\n<td><\/td>\r\n<td>Pennsylvania<\/td>\r\n<td>213<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Indiana<\/td>\r\n<td>220<\/td>\r\n<td><\/td>\r\n<td>Rhode Island<\/td>\r\n<td>165<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Iowa<\/td>\r\n<td>163<\/td>\r\n<td><\/td>\r\n<td>South Carolina<\/td>\r\n<td>155<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Kansas<\/td>\r\n<td>146<\/td>\r\n<td><\/td>\r\n<td>South Dakota<\/td>\r\n<td>154<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Kentucky<\/td>\r\n<td>149<\/td>\r\n<td><\/td>\r\n<td>Tennessee<\/td>\r\n<td>196<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Louisiana<\/td>\r\n<td>144<\/td>\r\n<td><\/td>\r\n<td>Texas<\/td>\r\n<td>186<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Maine<\/td>\r\n<td>165<\/td>\r\n<td><\/td>\r\n<td>Utah<\/td>\r\n<td>155<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Maryland<\/td>\r\n<td>199<\/td>\r\n<td><\/td>\r\n<td>Vermont<\/td>\r\n<td>124<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Massachusetts<\/td>\r\n<td>195<\/td>\r\n<td><\/td>\r\n<td>Virginia<\/td>\r\n<td>179<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Michigan<\/td>\r\n<td>188<\/td>\r\n<td><\/td>\r\n<td>Washington<\/td>\r\n<td>173<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Minnesota<\/td>\r\n<td>140<\/td>\r\n<td><\/td>\r\n<td>West Virginia<\/td>\r\n<td>150<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Mississippi<\/td>\r\n<td>146<\/td>\r\n<td><\/td>\r\n<td>Wisconsin<\/td>\r\n<td>211<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Missouri<\/td>\r\n<td>211<\/td>\r\n<td><\/td>\r\n<td>Wyoming<\/td>\r\n<td>134<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>Symbol<\/td>\r\n<td><\/td>\r\n<td>Description<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>difference between the population means<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>population mean of Group 1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>sample standard deviation of Group 1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>sample size of Group 1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>sample mean of Group 2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>difference between the sample means<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>sample mean of Group 1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>population mean of Group 2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>sample size of Group 2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>sample standard deviation of Group 2<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>Group 1:\r\n\r\n<em>smoke_now<\/em> = Yes\r\n\r\nMothers who smoked during pregnancy<\/td>\r\n<td>Group 2:\r\n\r\n<em>smoke_now<\/em> = No\r\n\r\nMothers who did not smoke during pregnancy<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Sample Mean<\/strong><\/td>\r\n<td>114<\/td>\r\n<td>\u00a0= 123<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Sample Standard Deviation<\/strong><\/td>\r\n<td>= 18.2<\/td>\r\n<td>= 17.3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Sample Size<\/strong><\/td>\r\n<td>= 480<\/td>\r\n<td>= 733<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>Group 1: Female Professors<\/td>\r\n<td>Group 2: Male Professors<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Sample Size<\/strong><\/td>\r\n<td>40<\/td>\r\n<td>53<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Sample Mean Course Evaluation Score<\/strong><\/td>\r\n<td>3.79<\/td>\r\n<td>4.01<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Sample Standard Deviation<\/strong><\/td>\r\n<td>0.51<\/td>\r\n<td>0.53<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>Community College Transfer (Group 1)<\/td>\r\n<td>No Transfer (Group 2)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Sample Size<\/strong><\/td>\r\n<td>267<\/td>\r\n<td>1176<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Sample Mean Time to Graduate, in Years<\/strong><\/td>\r\n<td>5.37<\/td>\r\n<td>4.45<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Sample Standard Deviation Time to Graduate, in Years<\/strong><\/td>\r\n<td>1.175<\/td>\r\n<td>1.001<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>gestation<\/td>\r\n<td>smoke<\/td>\r\n<td>smoke_now<\/td>\r\n<td>age<\/td>\r\n<td>wt<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>284<\/td>\r\n<td>never<\/td>\r\n<td>No<\/td>\r\n<td>27<\/td>\r\n<td>120<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>282<\/td>\r\n<td>never<\/td>\r\n<td>No<\/td>\r\n<td>33<\/td>\r\n<td>113<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>279<\/td>\r\n<td>now<\/td>\r\n<td>Yes<\/td>\r\n<td>28<\/td>\r\n<td>128<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>282<\/td>\r\n<td>now<\/td>\r\n<td>Yes<\/td>\r\n<td>23<\/td>\r\n<td>108<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>286<\/td>\r\n<td>until current pregnancy<\/td>\r\n<td>No<\/td>\r\n<td>25<\/td>\r\n<td>136<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>244<\/td>\r\n<td>never<\/td>\r\n<td>No<\/td>\r\n<td>33<\/td>\r\n<td>138<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>245<\/td>\r\n<td>never<\/td>\r\n<td>No<\/td>\r\n<td>23<\/td>\r\n<td>132<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>289<\/td>\r\n<td>never<\/td>\r\n<td>No<\/td>\r\n<td>25<\/td>\r\n<td>120<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>299<\/td>\r\n<td>now<\/td>\r\n<td>Yes<\/td>\r\n<td>30<\/td>\r\n<td>143<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>351<\/td>\r\n<td>once did, not now<\/td>\r\n<td>No<\/td>\r\n<td>27<\/td>\r\n<td>140<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>Group 1:\r\n\r\n<em>smoke_now<\/em> = Yes\r\n\r\nMothers who smoked during pregnancy<\/td>\r\n<td>Group 2:\r\n\r\n<em>smoke_now<\/em> = No\r\n\r\nMothers who did not smoke during pregnancy<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Sample Mean<\/strong><\/td>\r\n<td><\/td>\r\n<td>&nbsp;\r\n\r\n= ____<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Sample Standard Deviation<\/strong><\/td>\r\n<td>&nbsp;\r\n\r\n= ______\r\n\r\n&nbsp;<\/td>\r\n<td>&nbsp;\r\n\r\n= ______\r\n\r\n&nbsp;<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>&nbsp;\r\n\r\n<strong>Sample Size<\/strong><\/td>\r\n<td>&nbsp;\r\n\r\n= ______\r\n\r\n&nbsp;<\/td>\r\n<td>&nbsp;\r\n\r\n= _____\r\n\r\n&nbsp;<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div style=\"text-align: left;\" align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>Skill or Concept: I can . . .<\/td>\r\n<td>Questions to check your understanding<\/td>\r\n<td>Rating\r\nfrom 1 to 5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use appropriate notation to represent the sample mean, sample standard deviation, and sample size for multiple groups.<\/td>\r\n<td>1, 2<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write an expression that represents the difference between two sample means and the difference between two population means.<\/td>\r\n<td>3<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Verify that conditions are met for a two-sample t-test for independent samples.<\/td>\r\n<td>4<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Calculate the standard error for a sampling distribution and interpret its meaning.<\/td>\r\n<td>5<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use descriptive statistics to describe the difference between two sample means and interpret its meaning.<\/td>\r\n<td>6, 7<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<img class=\"alignnone wp-image-1982\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26200106\/Picture39-300x123.jpg\" alt=\"text reading &quot;Bias in selection. Selection of mothers by smoking habit may result in a study population consisting of two groups that are dissimilar in other respects. The basic problem is that some well-known risk factors affecting mortality are also independently related to the frequency of smoking.&quot;\" width=\"900\" height=\"369\" \/> <img class=\"alignnone wp-image-1983\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26200112\/Picture401-300x196.png\" alt=\"The output from a data analysis tool. In the top left, there is a heading reading \u201cDescriptive Statistics.\u201d Beneath it is a table with columns \u201cGroup,\u201d \u201cSample Size,\u201d \u201cMean,\u201d and \u201cStandard Deviation.\u201d The first row reads \u201cMale Politicians\u201d under Group, 30 under Sample Size, 10.7 under Mean, 26.3 under standard deviation. The second row reads \u201cFemale Politicians\u201d under Group, 30 under Sample Size, -1.1 under Mean, and 27.9 under standard deviation. Beneath this table is another table, titled \u201cTest Statistic.\u201d It has columns \u201cObserved Difference,\u201d \u201cStandard Error,\u201d \u201cTest Statistic t,\u201d and \u201cdt.\u201d Their values are 11.8, 7.0, 1.681, and 57.8, respectively. There is another table beneath this labeled \u201cHypothesis Test.\u201d It has the columns \u201cPopulation Parameter,\u201d \u201cNull Hypothesis,\u201d \u201cAlternative Hypothesis,\u201d \u201cTest Statistic t,\u201d and \u201cP-value.\u201d Under population parameter, it reads \u201cDifference mu sub one - mu sub two,\u201d under null hypothesis, it reads \u201cmu sub one - mu sub two = 0,\u201d under alternative hypothesis, it reads \u201cmu sub one - mu sub two does not equal 0,\u201d under test statistic t, it reads 1.681, and under p-value, it reads 0.0981. To the right of these tables is a box plot labeled \u201cDominance\u201d on the y-axis. For \u201cMale Politicians,\u201d the low end is at approximately -40 and the high end is at approximately 50. The low point of the box is at approximately 10 and the high end is at approximately 30. The middle line is at approximately 20. For \u201cFemale Politicians,\u201d the low end is at approximately -40 and the high end is at approximately 70. The low point of the box is at approximately -25 and the high point is at approximately 20. The middle line is at approximately 0. Beneath this box plot and the tables, there is a graph titled \u201ct Distribution with dt = 57.8\u201d with a subheading reading \u201cH sub 0: mu sub 1 equals mu sub 2, H sub a: mu sub 1 does not equal mu sub 2. Test Statistic: t = 1.681, P-value = 0.0981.\u201d The graph below shows a curve with a peak centered on approximately 0. There are dotted vertical lines at -1.68 and 1.68. The area outside these lines under the curve is shaded and on each side is labeled 0.0491. The area between the lines under the curve is a lighter shade and is labeled 0.9019.\" width=\"880\" height=\"575\" \/>\r\n\r\nGlossary\r\n<dl id=\"fs-id1170572229168\" class=\"definition\">\r\n \t<dt>two-sample t-test<\/dt>\r\n \t<dd id=\"fs-id1170572229174\">a hypothesis test for comparing two population means.<\/dd>\r\n<\/dl>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td><strong>State<\/strong><\/td>\n<td><strong>Average Daily Screen Time <\/strong><\/p>\n<p><strong>(in minutes)<\/strong><\/td>\n<td><strong>\u00a0<\/strong><\/td>\n<td><strong>State<\/strong><\/td>\n<td><strong>Average Daily Screen Time (in minutes)<\/strong><\/td>\n<\/tr>\n<tr>\n<td>Alabama<\/td>\n<td>170<\/td>\n<td><\/td>\n<td>Montana<\/td>\n<td>154<\/td>\n<\/tr>\n<tr>\n<td>Alaska<\/td>\n<td>134<\/td>\n<td><\/td>\n<td>Nebraska<\/td>\n<td>182<\/td>\n<\/tr>\n<tr>\n<td>Arizona<\/td>\n<td>276<\/td>\n<td><\/td>\n<td>Nevada<\/td>\n<td>262<\/td>\n<\/tr>\n<tr>\n<td>Arkansas<\/td>\n<td>145<\/td>\n<td><\/td>\n<td>New Hampshire<\/td>\n<td>135<\/td>\n<\/tr>\n<tr>\n<td>California<\/td>\n<td>204<\/td>\n<td><\/td>\n<td>New Jersey<\/td>\n<td>182<\/td>\n<\/tr>\n<tr>\n<td>Colorado<\/td>\n<td>166<\/td>\n<td><\/td>\n<td>New Mexico<\/td>\n<td>177<\/td>\n<\/tr>\n<tr>\n<td>Connecticut<\/td>\n<td>262<\/td>\n<td><\/td>\n<td>New York<\/td>\n<td>206<\/td>\n<\/tr>\n<tr>\n<td>Delaware<\/td>\n<td>166<\/td>\n<td><\/td>\n<td>North Carolina<\/td>\n<td>205<\/td>\n<\/tr>\n<tr>\n<td>Florida<\/td>\n<td>213<\/td>\n<td><\/td>\n<td>North Dakota<\/td>\n<td>192<\/td>\n<\/tr>\n<tr>\n<td>Georgia<\/td>\n<td>198<\/td>\n<td><\/td>\n<td>Ohio<\/td>\n<td>231<\/td>\n<\/tr>\n<tr>\n<td>Hawaii<\/td>\n<td>133<\/td>\n<td><\/td>\n<td>Oklahoma<\/td>\n<td>131<\/td>\n<\/tr>\n<tr>\n<td>Idaho<\/td>\n<td>161<\/td>\n<td><\/td>\n<td>Oregon<\/td>\n<td>132<\/td>\n<\/tr>\n<tr>\n<td>Illinois<\/td>\n<td>220<\/td>\n<td><\/td>\n<td>Pennsylvania<\/td>\n<td>213<\/td>\n<\/tr>\n<tr>\n<td>Indiana<\/td>\n<td>220<\/td>\n<td><\/td>\n<td>Rhode Island<\/td>\n<td>165<\/td>\n<\/tr>\n<tr>\n<td>Iowa<\/td>\n<td>163<\/td>\n<td><\/td>\n<td>South Carolina<\/td>\n<td>155<\/td>\n<\/tr>\n<tr>\n<td>Kansas<\/td>\n<td>146<\/td>\n<td><\/td>\n<td>South Dakota<\/td>\n<td>154<\/td>\n<\/tr>\n<tr>\n<td>Kentucky<\/td>\n<td>149<\/td>\n<td><\/td>\n<td>Tennessee<\/td>\n<td>196<\/td>\n<\/tr>\n<tr>\n<td>Louisiana<\/td>\n<td>144<\/td>\n<td><\/td>\n<td>Texas<\/td>\n<td>186<\/td>\n<\/tr>\n<tr>\n<td>Maine<\/td>\n<td>165<\/td>\n<td><\/td>\n<td>Utah<\/td>\n<td>155<\/td>\n<\/tr>\n<tr>\n<td>Maryland<\/td>\n<td>199<\/td>\n<td><\/td>\n<td>Vermont<\/td>\n<td>124<\/td>\n<\/tr>\n<tr>\n<td>Massachusetts<\/td>\n<td>195<\/td>\n<td><\/td>\n<td>Virginia<\/td>\n<td>179<\/td>\n<\/tr>\n<tr>\n<td>Michigan<\/td>\n<td>188<\/td>\n<td><\/td>\n<td>Washington<\/td>\n<td>173<\/td>\n<\/tr>\n<tr>\n<td>Minnesota<\/td>\n<td>140<\/td>\n<td><\/td>\n<td>West Virginia<\/td>\n<td>150<\/td>\n<\/tr>\n<tr>\n<td>Mississippi<\/td>\n<td>146<\/td>\n<td><\/td>\n<td>Wisconsin<\/td>\n<td>211<\/td>\n<\/tr>\n<tr>\n<td>Missouri<\/td>\n<td>211<\/td>\n<td><\/td>\n<td>Wyoming<\/td>\n<td>134<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td>Symbol<\/td>\n<td><\/td>\n<td>Description<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>difference between the population means<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>population mean of Group 1<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>sample standard deviation of Group 1<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>sample size of Group 1<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>sample mean of Group 2<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>difference between the sample means<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>sample mean of Group 1<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>population mean of Group 2<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>sample size of Group 2<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>sample standard deviation of Group 2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td><\/td>\n<td>Group 1:<\/p>\n<p><em>smoke_now<\/em> = Yes<\/p>\n<p>Mothers who smoked during pregnancy<\/td>\n<td>Group 2:<\/p>\n<p><em>smoke_now<\/em> = No<\/p>\n<p>Mothers who did not smoke during pregnancy<\/td>\n<\/tr>\n<tr>\n<td><strong>Sample Mean<\/strong><\/td>\n<td>114<\/td>\n<td>\u00a0= 123<\/td>\n<\/tr>\n<tr>\n<td><strong>Sample Standard Deviation<\/strong><\/td>\n<td>= 18.2<\/td>\n<td>= 17.3<\/td>\n<\/tr>\n<tr>\n<td><strong>Sample Size<\/strong><\/td>\n<td>= 480<\/td>\n<td>= 733<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<tbody>\n<tr>\n<td><\/td>\n<td>Group 1: Female Professors<\/td>\n<td>Group 2: Male Professors<\/td>\n<\/tr>\n<tr>\n<td><strong>Sample Size<\/strong><\/td>\n<td>40<\/td>\n<td>53<\/td>\n<\/tr>\n<tr>\n<td><strong>Sample Mean Course Evaluation Score<\/strong><\/td>\n<td>3.79<\/td>\n<td>4.01<\/td>\n<\/tr>\n<tr>\n<td><strong>Sample Standard Deviation<\/strong><\/td>\n<td>0.51<\/td>\n<td>0.53<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<tbody>\n<tr>\n<td><\/td>\n<td>Community College Transfer (Group 1)<\/td>\n<td>No Transfer (Group 2)<\/td>\n<\/tr>\n<tr>\n<td><strong>Sample Size<\/strong><\/td>\n<td>267<\/td>\n<td>1176<\/td>\n<\/tr>\n<tr>\n<td><strong>Sample Mean Time to Graduate, in Years<\/strong><\/td>\n<td>5.37<\/td>\n<td>4.45<\/td>\n<\/tr>\n<tr>\n<td><strong>Sample Standard Deviation Time to Graduate, in Years<\/strong><\/td>\n<td>1.175<\/td>\n<td>1.001<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<table>\n<tbody>\n<tr>\n<td>gestation<\/td>\n<td>smoke<\/td>\n<td>smoke_now<\/td>\n<td>age<\/td>\n<td>wt<\/td>\n<\/tr>\n<tr>\n<td>284<\/td>\n<td>never<\/td>\n<td>No<\/td>\n<td>27<\/td>\n<td>120<\/td>\n<\/tr>\n<tr>\n<td>282<\/td>\n<td>never<\/td>\n<td>No<\/td>\n<td>33<\/td>\n<td>113<\/td>\n<\/tr>\n<tr>\n<td>279<\/td>\n<td>now<\/td>\n<td>Yes<\/td>\n<td>28<\/td>\n<td>128<\/td>\n<\/tr>\n<tr>\n<td>282<\/td>\n<td>now<\/td>\n<td>Yes<\/td>\n<td>23<\/td>\n<td>108<\/td>\n<\/tr>\n<tr>\n<td>286<\/td>\n<td>until current pregnancy<\/td>\n<td>No<\/td>\n<td>25<\/td>\n<td>136<\/td>\n<\/tr>\n<tr>\n<td>244<\/td>\n<td>never<\/td>\n<td>No<\/td>\n<td>33<\/td>\n<td>138<\/td>\n<\/tr>\n<tr>\n<td>245<\/td>\n<td>never<\/td>\n<td>No<\/td>\n<td>23<\/td>\n<td>132<\/td>\n<\/tr>\n<tr>\n<td>289<\/td>\n<td>never<\/td>\n<td>No<\/td>\n<td>25<\/td>\n<td>120<\/td>\n<\/tr>\n<tr>\n<td>299<\/td>\n<td>now<\/td>\n<td>Yes<\/td>\n<td>30<\/td>\n<td>143<\/td>\n<\/tr>\n<tr>\n<td>351<\/td>\n<td>once did, not now<\/td>\n<td>No<\/td>\n<td>27<\/td>\n<td>140<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td><\/td>\n<td>Group 1:<\/p>\n<p><em>smoke_now<\/em> = Yes<\/p>\n<p>Mothers who smoked during pregnancy<\/td>\n<td>Group 2:<\/p>\n<p><em>smoke_now<\/em> = No<\/p>\n<p>Mothers who did not smoke during pregnancy<\/td>\n<\/tr>\n<tr>\n<td><strong>Sample Mean<\/strong><\/td>\n<td><\/td>\n<td>&nbsp;<\/p>\n<p>= ____<\/td>\n<\/tr>\n<tr>\n<td><strong>Sample Standard Deviation<\/strong><\/td>\n<td>&nbsp;<\/p>\n<p>= ______<\/p>\n<p>&nbsp;<\/td>\n<td>&nbsp;<\/p>\n<p>= ______<\/p>\n<p>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>&nbsp;<\/p>\n<p><strong>Sample Size<\/strong><\/td>\n<td>&nbsp;<\/p>\n<p>= ______<\/p>\n<p>&nbsp;<\/td>\n<td>&nbsp;<\/p>\n<p>= _____<\/p>\n<p>&nbsp;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"text-align: left; margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td>Skill or Concept: I can . . .<\/td>\n<td>Questions to check your understanding<\/td>\n<td>Rating<br \/>\nfrom 1 to 5<\/td>\n<\/tr>\n<tr>\n<td>Use appropriate notation to represent the sample mean, sample standard deviation, and sample size for multiple groups.<\/td>\n<td>1, 2<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write an expression that represents the difference between two sample means and the difference between two population means.<\/td>\n<td>3<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Verify that conditions are met for a two-sample t-test for independent samples.<\/td>\n<td>4<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Calculate the standard error for a sampling distribution and interpret its meaning.<\/td>\n<td>5<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Use descriptive statistics to describe the difference between two sample means and interpret its meaning.<\/td>\n<td>6, 7<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1982\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26200106\/Picture39-300x123.jpg\" alt=\"text reading &quot;Bias in selection. Selection of mothers by smoking habit may result in a study population consisting of two groups that are dissimilar in other respects. The basic problem is that some well-known risk factors affecting mortality are also independently related to the frequency of smoking.&quot;\" width=\"900\" height=\"369\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1983\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26200112\/Picture401-300x196.png\" alt=\"The output from a data analysis tool. In the top left, there is a heading reading \u201cDescriptive Statistics.\u201d Beneath it is a table with columns \u201cGroup,\u201d \u201cSample Size,\u201d \u201cMean,\u201d and \u201cStandard Deviation.\u201d The first row reads \u201cMale Politicians\u201d under Group, 30 under Sample Size, 10.7 under Mean, 26.3 under standard deviation. The second row reads \u201cFemale Politicians\u201d under Group, 30 under Sample Size, -1.1 under Mean, and 27.9 under standard deviation. Beneath this table is another table, titled \u201cTest Statistic.\u201d It has columns \u201cObserved Difference,\u201d \u201cStandard Error,\u201d \u201cTest Statistic t,\u201d and \u201cdt.\u201d Their values are 11.8, 7.0, 1.681, and 57.8, respectively. There is another table beneath this labeled \u201cHypothesis Test.\u201d It has the columns \u201cPopulation Parameter,\u201d \u201cNull Hypothesis,\u201d \u201cAlternative Hypothesis,\u201d \u201cTest Statistic t,\u201d and \u201cP-value.\u201d Under population parameter, it reads \u201cDifference mu sub one - mu sub two,\u201d under null hypothesis, it reads \u201cmu sub one - mu sub two = 0,\u201d under alternative hypothesis, it reads \u201cmu sub one - mu sub two does not equal 0,\u201d under test statistic t, it reads 1.681, and under p-value, it reads 0.0981. To the right of these tables is a box plot labeled \u201cDominance\u201d on the y-axis. For \u201cMale Politicians,\u201d the low end is at approximately -40 and the high end is at approximately 50. The low point of the box is at approximately 10 and the high end is at approximately 30. The middle line is at approximately 20. For \u201cFemale Politicians,\u201d the low end is at approximately -40 and the high end is at approximately 70. The low point of the box is at approximately -25 and the high point is at approximately 20. The middle line is at approximately 0. Beneath this box plot and the tables, there is a graph titled \u201ct Distribution with dt = 57.8\u201d with a subheading reading \u201cH sub 0: mu sub 1 equals mu sub 2, H sub a: mu sub 1 does not equal mu sub 2. Test Statistic: t = 1.681, P-value = 0.0981.\u201d The graph below shows a curve with a peak centered on approximately 0. There are dotted vertical lines at -1.68 and 1.68. The area outside these lines under the curve is shaded and on each side is labeled 0.0491. The area between the lines under the curve is a lighter shade and is labeled 0.9019.\" width=\"880\" height=\"575\" \/><\/p>\n<p>Glossary<\/p>\n<dl id=\"fs-id1170572229168\" class=\"definition\">\n<dt>two-sample t-test<\/dt>\n<dd id=\"fs-id1170572229174\">a hypothesis test for comparing two population means.<\/dd>\n<\/dl>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":23592,"menu_order":44,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1981","chapter","type-chapter","status-publish","hentry"],"part":704,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/1981","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/23592"}],"version-history":[{"count":5,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/1981\/revisions"}],"predecessor-version":[{"id":2974,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/1981\/revisions\/2974"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/704"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/1981\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=1981"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=1981"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=1981"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=1981"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}