{"id":4941,"date":"2022-08-16T23:11:58","date_gmt":"2022-08-16T23:11:58","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=4941"},"modified":"2022-08-17T18:42:49","modified_gmt":"2022-08-17T18:42:49","slug":"13c-inclass","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/13c-inclass\/","title":{"raw":"13C InClass","rendered":"13C InClass"},"content":{"raw":"Recall the maternal smoking study presented in Preview Assignment 13.C.\r\n\r\nResearchers wanted to study the difference in birth weight of babies born to mothers\u00a0 who smoked during pregnancy (smoke_now = yes) and mothers who did not smoke\u00a0 during pregnancy.\r\n
\r\n

Question 1<\/h3>\r\n1) Discuss the differences that you saw in the visualization between the birth weights of babies born to women who smoked during pregnancy compared to mothers who did\u00a0 not smoke during pregnancy.\r\n\r\n<\/div>\r\n
\r\n

Question 2<\/h3>\r\n2) How can we make an inference about the difference when the population refers to\u00a0 all pregnant women?\r\n\r\n<\/div>\r\nIn the previous in-class activity, you reviewed and applied the steps to perform a one sample t-test (a hypothesis test about a population mean). We can apply the same\u00a0 steps to analyze and test a hypothesis about the difference in means for two\u00a0 independent populations. A hypothesis test for comparing two population means is often\u00a0 referred to as a two-sample t-test.\r\n\r\nIn the preview assignment, you verified that the assumptions for a two-sample t-test\u00a0 were met for the maternal smoking study. We know that the two samples were\u00a0 independent, representative of the populations of interest, and large.\r\n
\r\n

Question 3<\/h3>\r\n3) Group 1 consists of mothers who smoked during pregnancy, and Group 2 consists\u00a0 of mothers who did not smoke during pregnancy.\r\n\r\na) What is the parameter of interest?\r\n\r\nb) Write the null and alternative hypotheses, with proper notations for each.\r\n\r\n<\/div>\r\nThe test statistic to compare two population means is calculated using the following\u00a0 formula:\r\n\r\n[latex]t=\\frac{estimate\\;of\\;parameter-null\\;hypothesis\\;value}{standard\\;error}=\\frac{(\\bar{x}_{1}-\\bar{x}_{2})-(\\mu_{1}-\\mu_{2})}{\\sqrt{\\frac{s^{2}_{1}}{n_{1}}+\\frac{s^{2}_{2}}{n_{2}}}}[\/latex]\r\n
\r\n

Question 4<\/h3>\r\n4) Use the DCMP Compare Two Population Means tool at\u00a0https:\/\/dcmathpathways.shinyapps.io\/2sample_mean\/ to complete the test. Select\u00a0 \u201cSummary Statistics\u201d and enter the values from the following table:\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\nGroup 1:\r\n\r\nsmoke_now = Yes\r\n\r\nMothers who\r\n\r\nsmoked during\r\n\r\npregnancy<\/td>\r\nGroup 2:\r\n\r\nsmoke_now = No\r\n\r\nMothers who did not\u00a0 smoke during\r\n\r\npregnancy<\/td>\r\n<\/tr>\r\n
Sample Mean<\/td>\r\n[latex]\\bar{x}_{1}[\/latex] = 114<\/td>\r\n[latex]\\bar{x}_{2}[\/latex] = 123<\/td>\r\n<\/tr>\r\n
Sample Standard\u00a0 Deviation<\/td>\r\n[latex]s_{1}[\/latex] = 18.2<\/td>\r\n[latex]s_{2}[\/latex]\u00a0= 17.3<\/td>\r\n<\/tr>\r\n
Sample Size<\/td>\r\n[latex]n_{1}[\/latex] = 480<\/td>\r\n[latex]n_{2}[\/latex]\u00a0= 733<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\na) What is the value of the test statistic?\r\n\r\nb) What is the P-value?\r\n\r\nc) Given a 5% significance level, what do you conclude? Write your conclusion in context and support your answer.\r\n\r\nd) Is this conclusion consistent with what you concluded using only the\u00a0 visualizations in Question 1?\r\n\r\n<\/div>\r\n
\r\n

Question 5<\/h3>\r\n5) We often learn more from constructing confidence intervals than from the hypothesis\u00a0 test because it shows a range of plausible values for the difference between the\u00a0 population means.\r\n\r\na) Use the same DCMP tool to calculate and interpret the 95% confidence\u00a0 interval to estimate the difference in the population means. Round your\u00a0 answer to the nearest hundredth.\r\n\r\nb) Interpret the result. Include the relevance of 0 in your description.\r\n\r\n<\/div>\r\n
\r\n

Question 6<\/h3>\r\n6) An original article published in 1972 in the Journal of Epidemiology concluded that\u00a0 there was \u201ca positive association between maternal cigarette smoking and reduced\u00a0 infant birth weight.\u201d\r\n\r\na) Why did the authors choose the word \u201cassociation\u201d rather than \u201ccausation?\u201d\r\n\r\nb) Read the following excerpt from the same article. Discuss how this statement\u00a0 might impact your conclusion.\r\n\r\n\"text\r\n\r\n<\/div>","rendered":"

Recall the maternal smoking study presented in Preview Assignment 13.C.<\/p>\n

Researchers wanted to study the difference in birth weight of babies born to mothers\u00a0 who smoked during pregnancy (smoke_now = yes) and mothers who did not smoke\u00a0 during pregnancy.<\/p>\n

\n

Question 1<\/h3>\n

1) Discuss the differences that you saw in the visualization between the birth weights of babies born to women who smoked during pregnancy compared to mothers who did\u00a0 not smoke during pregnancy.<\/p>\n<\/div>\n

\n

Question 2<\/h3>\n

2) How can we make an inference about the difference when the population refers to\u00a0 all pregnant women?<\/p>\n<\/div>\n

In the previous in-class activity, you reviewed and applied the steps to perform a one sample t-test (a hypothesis test about a population mean). We can apply the same\u00a0 steps to analyze and test a hypothesis about the difference in means for two\u00a0 independent populations. A hypothesis test for comparing two population means is often\u00a0 referred to as a two-sample t-test.<\/p>\n

In the preview assignment, you verified that the assumptions for a two-sample t-test\u00a0 were met for the maternal smoking study. We know that the two samples were\u00a0 independent, representative of the populations of interest, and large.<\/p>\n

\n

Question 3<\/h3>\n

3) Group 1 consists of mothers who smoked during pregnancy, and Group 2 consists\u00a0 of mothers who did not smoke during pregnancy.<\/p>\n

a) What is the parameter of interest?<\/p>\n

b) Write the null and alternative hypotheses, with proper notations for each.<\/p>\n<\/div>\n

The test statistic to compare two population means is calculated using the following\u00a0 formula:<\/p>\n

[latex]t=\\frac{estimate\\;of\\;parameter-null\\;hypothesis\\;value}{standard\\;error}=\\frac{(\\bar{x}_{1}-\\bar{x}_{2})-(\\mu_{1}-\\mu_{2})}{\\sqrt{\\frac{s^{2}_{1}}{n_{1}}+\\frac{s^{2}_{2}}{n_{2}}}}[\/latex]<\/p>\n

\n

Question 4<\/h3>\n

4) Use the DCMP Compare Two Population Means tool at\u00a0https:\/\/dcmathpathways.shinyapps.io\/2sample_mean\/ to complete the test. Select\u00a0 \u201cSummary Statistics\u201d and enter the values from the following table:<\/p>\n

\n\n\n\n\n\n\n
<\/td>\nGroup 1:<\/p>\n

smoke_now = Yes<\/p>\n

Mothers who<\/p>\n

smoked during<\/p>\n

pregnancy<\/td>\n

Group 2:<\/p>\n

smoke_now = No<\/p>\n

Mothers who did not\u00a0 smoke during<\/p>\n

pregnancy<\/td>\n<\/tr>\n

Sample Mean<\/td>\n[latex]\\bar{x}_{1}[\/latex] = 114<\/td>\n[latex]\\bar{x}_{2}[\/latex] = 123<\/td>\n<\/tr>\n
Sample Standard\u00a0 Deviation<\/td>\n[latex]s_{1}[\/latex] = 18.2<\/td>\n[latex]s_{2}[\/latex]\u00a0= 17.3<\/td>\n<\/tr>\n
Sample Size<\/td>\n[latex]n_{1}[\/latex] = 480<\/td>\n[latex]n_{2}[\/latex]\u00a0= 733<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

a) What is the value of the test statistic?<\/p>\n

b) What is the P-value?<\/p>\n

c) Given a 5% significance level, what do you conclude? Write your conclusion in context and support your answer.<\/p>\n

d) Is this conclusion consistent with what you concluded using only the\u00a0 visualizations in Question 1?<\/p>\n<\/div>\n

\n

Question 5<\/h3>\n

5) We often learn more from constructing confidence intervals than from the hypothesis\u00a0 test because it shows a range of plausible values for the difference between the\u00a0 population means.<\/p>\n

a) Use the same DCMP tool to calculate and interpret the 95% confidence\u00a0 interval to estimate the difference in the population means. Round your\u00a0 answer to the nearest hundredth.<\/p>\n

b) Interpret the result. Include the relevance of 0 in your description.<\/p>\n<\/div>\n

\n

Question 6<\/h3>\n

6) An original article published in 1972 in the Journal of Epidemiology concluded that\u00a0 there was \u201ca positive association between maternal cigarette smoking and reduced\u00a0 infant birth weight.\u201d<\/p>\n

a) Why did the authors choose the word \u201cassociation\u201d rather than \u201ccausation?\u201d<\/p>\n

b) Read the following excerpt from the same article. Discuss how this statement\u00a0 might impact your conclusion.<\/p>\n

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