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(solution) Hi there! I'm using R script to answer these questions but I;m


Hi there! I'm using R script to answer these questions but I;m having some issues. Could you help please. Also, if you could provide me a copy of the R code generated that would be great, so that I can compare my results and see where I went wrong. Thank you


1. Consider a large population of families in which each family has exactly three

 

children. If the sexes of the three children in any family are independent of one

 

another, the number of male children in a randomly selected family will have a

 

binomial distribution based on three trials. In other words:

 

.

 

n x

 

P ( N males x | n 3, p 0.5) p (1 p ) n x dbinom ( x, n, p ) x Suppose a random sample of 160 families yields the results shown in the table

 

below. Use the formula above to fill in the expected frequencies in the table. Test

 

the null hypothesis that this sample comes from a population exhibiting the

 

outcomes expected under a binomial distribution with an equally likely chance of

 

having a male or female child (i.e. p=0.5). Show all work for full credit.

 

Number of

 

Male Children

 

Observed

 

Frequency

 

Expected

 

Frequency 0 1 2 3 14 66 64 16 2. (50 points total) Purina has decided to explore alternative diet recipes used in the

 

making of its turkey chow in order to find a formulation that maximizes turkey

 

weight gain. Four different diet formulations were compared to a control

 

formulation Purina currently has on the market. Your job is to see if the

 

formulations differ significantly from one another and present your findings to

 

Purina executives. Use the data below to answer the following questions.

 

turkey = data.frame(

 

group = c(

 

rep("control",6),

 

rep("diet1",6),

 

rep("diet2",6),

 

rep("diet3",6),

 

rep("diet4",6)),

 

weight = c(

 

4.1,3.3,3.1,4.2,3.6,4.4,

 

5.2,4.8,4.5,6.8,5.5,6.2,

 

6.3,6.5,7.2,7.4,7.8,6.7,

 

6.5,6.8,7.3,7.5,6.9,7.0, 9.5,9.6,9.2,9.1,9.8,9.1))

 

a. Provide a dynamite plot that shows the mean weight gain by treatment group,

 

the 95% CI around each mean, and symbols that indicate the degree of

 

statistical similarity between treatment groups.

 

b. Use Scheffe?s method to test the following hypotheses (show all work for full

 

credit):

 

i.

 

ii. control 1 diet1 diet2 diet3 diet4 4

 

1

 

2 diet1 diet2 1 diet3 diet4 2 c. One of the executives believes the assumptions required for the tests applied

 

above are not met and asks you to conduct a nonparametric test on these data

 

to further check if the group medians are statistically different from one another.

 

Conduct such a test, provide the results and state whether or not these results

 

are consistent with the findings derived above.

 


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