(Solved): 23. Cereal The data below show the sugar content (as a per- \( [\mathrm{T}] 2 \) centage of weight) ...

23. Cereal The data below show the sugar content (as a per- \( [\mathrm{T}] 2 \) centage of weight) of several national brands of children's and adults' cereals. Create and interpret a 95\% confidence interval for the difference in mean sugar content. Be sure to check the necessary assumptions and conditions. Children's cereals: \( 40.3,55,45.7,43.3,50.3,45.9 \), \( 53.5,43,44.2,44,47.4,44,33.6,55.1,48.8,50.4,37.8 \), \( 60.3,46.6 \) Adults' cereals: 20, 30.2, 2.2, 7.5, 4.4, 22.2, 16.6, 14.5, \( 21.4,3.3,6.6,7.8,10.6,16.2,14.5,4.1,15.8,4.1,2.4 \), \( 3.5,8.5,10,1,4.4,1.3,8.1,4.7,18.4 \) Turn to page 629 in your textbook and read question 23. Answer the questions below based on the data presented in that question. We are testing to see if there is a difference in mean sugar content between children's and adults' cereals. The Minitab output is posted in a separate file on Moodle. Do not perform any unnecessary calculations. Check, in the context of the question, the sample size assumption. Include in your answer the name of the condition you are checking. Note that the independent group assumption and independence assumption are met as long as the brands selected are representative of all children's and adult cereals. And we need to check the sample size assumption since we do not know the shape of the distributions for sugar content. State the appropriate hypotheses (Ho and \( \mathrm{Ha} \) ) in symbols and define the parameters in context. Identify the test statistic and p-value from the Minitab output. Briefly assess the strength of the evidence. State your conclusion in the context of the problem. The \( 95 \% \) confidence interval is given on the output. Complete the interpretation of the confidence interval. If the assumptions are met and the distribution of sugar content are normal (or only slightly skewed), we are \( 95 \% \) confident that the sugar content of children's cereals is between \( 32.15 \) and \( 40.82 \) grams adult cereal, for the population of all Based on the confidence interval, what can you say about the difference in the mean sugar content between the two types of cereals? Explain briefly. What significance level are you assuming for your answer to the previous question [QUESTION 8]? Leave your answer as a decimal (NOT a percent). Answer: