Question

The data below shows the sugar content in grams of several brands of​ children's and​ adults' cereals. Create and interpret a​ 95% confidence interval for the difference in the mean sugar​ content,

mu Subscript Upper C Baseline minus mu Subscript Upper AμC−μA.

Be sure to check the necessary assumptions and conditions.​(Note: Do not assume that the variances of the two data sets are​ equal.)

Full data set

​Children's cereal: 43.8 comma43.8, 59.2 comma59.2, 48.2 comma48.2, 44.7 comma44.7, 53 comma53, 45.1 comma45.1, 51.1 comma51.1, 41.3 comma41.3, 43.3 comma43.3, 41.6 comma41.6, 49 comma49, 40.7 comma40.7, 39.3 comma39.3, 57.1 comma57.1, 47 comma47, 51.6 comma51.6, 39 comma39, 59.4 comma59.4, 40.7 comma40.7, 32.732.7

​Adults' cereal: 21.2 comma21.2, 27 comma27, 1.1 comma1.1, 9.9 comma9.9, 4.5 comma4.5, 21.6 comma21.6, 15.1 comma15.1, 13.3 comma13.3, 21.8 comma21.8, 7.6 comma7.6, 8.2 comma8.2, 13.9 comma13.9, 19.6 comma19.6, 12.6 comma12.6, 3.2 comma3.2, 15.3 comma15.3, 2.5 comma2.5, 3 comma3, 3.6 comma3.6, 9.8 comma9.8, 10.8 comma10.8, 4.8 comma4.8, 4.2 comma4.2, 2.1 comma2.1, 5.8 comma5.8, 2.8 comma2.8, 16.8 comma16.8, 8.3 comma8.3, 15.2 comma15.2, 11.4

Answer 1

We are given statistics for a two-sample t-test having unequal variance. First, we will find the degree of freedom and the respective critical value. After that, a 95% confidence interval can be developed.