All the pictures are attached below:

Rat chow is formulated to meet the animals' complete nutritional needs in a way that maintains optimal health.

A study was designed to compare the weights of rats who had access to rat chow only and those who had access to rat chow and cafeteria food.

Adult male rats who had been raised under identical conditions were randomly assigned to have access to rat chow only or rat chow and access to a variety of foods from the campus cafeteria that were high in fat or sugar for 18 hours a day.

All of the rats could eat as much rat chow as they wanted.

The rats in the group with access to cafeteria food could also eat as much as they wanted during the 18 hours of each day that they had access to the cafeteria food.

After several weeks, the rats' weights were measured.

The investigators hypothesized that the rats with access to cafeteria food would weigh more, on average, than the rats with access only to rat chow.

The way the randomization was done, 15 rats were assigned to have access to art chow and cafeteria food (group chow_cafe) and 19 rats were assigned to rat chow only (group chow_only).

1.1 Based on these box plots, are the distributions of the rats' weights roughly symmetric? please explain.

1.2 Here are the normal quantile plots and the Shapiro-Wilk tests for each of the groups:

Shapiro-Wilk P value = .9925

Shapiro-Wilk P value = .9269

Based on the normal quantile plots and the Shapiro Wilk tests, do these data contradict the

assumption that the populations of rats' weights follow normal curves,

at least approximately?

1.3 Based on your answers to questions 3.1 and 3.2, explain why the sampling distribution of x?chow-cafe?x?chow-onlyx is approximately normal

1.4 State the investigators' null and alternative hypotheses.

1.5 Using the summary statistics provided, calculate the estimated standard error of the difference of the sample averages x?chow-cafe?x?chow-onlyx

1.6 Calculate the test statistic. Show intermediate steps.

1.7 What is the P value for the investigators' alternative hypothesis?

1.8 Based on the P value, what do you conclude? [Use ?=0.05?=0.05.]

explain in a sentence that clearly communicates the results for a general audience.

1.9 What type of error might the investigators be making?Explain your reasoning

1.10 Do these data support the claim that the difference in the population mean weights could

be as small as 40 g ?

> epitab(preg_smoke, method = "oddsratio", conf. level = .95, oddsratio = "wald", pvalue = "chi2", correction = F) key part of output, reformatted full term po preterm p1 never smoke 3396 0. 90175252 168 0. 8235294 smoke all thru 370 0. 09824748 36 0. 1764706 oddsratio lower upper p. value never smoke 1. 000000 NA NA NA smoke all thru 1. 966795 1. 350927 2. 86343 0. 0003290114rats' weights rat chow and cafeteria food vs. rat chow only chow_cafe chow_only 800 - 700 - weights in grams 600 -800 normal quantile plot for chow_cafe group 700 weight in grams 600 O O O O O -1 O normal scores Shapiro-Wilk P value = .9925normal quantile plot for chow_only group O O 550 600 650 700 weight in grams -2 -1 O N normal scores> t.test(rats_diets$weight ~ rats_diets$group_ord, var.equal = FALSE, mu = 0, alternative = "two.sided", conf.level = .95) Welch Two Sample ttest data: rats_diets$weight by rats_diets$group_ord t = 4.2872, df = 26.077, pvalue = 0.0002192 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 44.51347 126.49004 sample estimates: mean in group chow_cafe mean in group chow_only 691.1333 605.6316 > t.test(rats_diets$weight ~ rats_diets$group_ord, var.equal = FALSE, mu = 0, alternative = "greater", conf.level = .95) Welch Two Sample ttest data: rats_diets$weight by rats_diets$group_ord t = 4.2872, df = 26.077, pvalue = 0.0001096 alternative hypothesis: true difference in means is greater than 0 95 percent confidence interval: 51.4897 Inf sample estimates: mean in group chow_cafe mean in group chow_only 691.1333 605.6316 Here are the summary statistics for these data: n average std deviation chow_cafe 15 691.13 g 63.41 g chow_on|y 19 605.63 g 49.64 g