Data Analysis

 

1. Consider the following data drawn independently from normally distributed populations: (You may find it useful to reference the appropriate table: z table or t table)

x−1x−1 = −1.6 x−2x−2 = −16.3
s12 = 8.9 s22 = 7.9
n1 = 23 n2 = 15

a. Construct the 95% confidence interval for the difference between the population means. Assume the population variances are unknown but equal. (Round final answers to 2 decimal places.)

2. Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. (You may find it useful to reference the appropriate table: z table or t table)

H0: μ1 − μ2 ≥ 0
HA: μ1 − μ2 < 0

x−1x−1 = 256 x−2x−2 = 269
s1 = 37 s2 = 15
n1 = 9 n2 = 9

a-1. Calculate the value of the test statistic under the assumption that the population variances are equal. (Negative value should be indicated by a minus sign. Round final answer to 3 decimal places.)

b-1. Calculate the value of the test statistic under the assumption that the population variances are unknown and are not equal. (Negative value should be indicated by a minus sign. Round final answer to 3 decimal places.)

 

 

 

 

3. Consider the following competing hypotheses: (You may find it useful to reference the appropriate table: z table or t table)

H0: μD ≥ 0; HA: μD < 0

d⎯⎯d¯ = −3.7, sD = 5.5, n = 16

The following results are obtained using matched samples from two normally distributed populations:

a-1. Calculate the value of the test statistic, assuming that the sample difference is normally distributed. (Negative value should be indicated by a minus sign. Round final answer to 3 decimal places.)

 

 

 

 

 

 

 

 

Sample Solution

Willows was a book intended for adults, then possibly the definitive childhood character from The Golden Age of Children’s Writing’ is Peter Pan. Again, there is a conflict arising from the adult perception of what it means to be a child, or if the subtext of the story is one intended for children as readers. Here, a wilful and spirited boy replaces the image of Pan as a horned, half man, half goat god. Fairies and mermaids replace the Nymphs of mythology, and the shepherds who worshipped Pan are now a tribe of lost boys. Peter Pan is first introduced when ‘Mrs. Darling is tidying up her children’s minds’ as Barrie describes’ a child’s’ mind, which is not only confused, … it keeps going round all the time’ (Location 84 of 2074, Peter Pan and Wendy, Kindle edition.) Which suggests the author ultimately regards the minds of children and the state of childhood as a separate and unordered state, in need of organisation. Like Mr. Darling, Barrie feels compelled to reinstate order. We learn Peter Pan comes from Neverland, a place where each child has their version of Neverland, seen in the moments before they go to sleep. Peter lives with the fairies and ‘when Children died he went part of the way with them so that they would not be frightened.’ Within the story, there are fights to the death, and a reference to Peter Pan thinning out the lost boys, though we do not know how this is achieved. The story suggests Peter kills for fun. If a literal interpretation, then he is cruel and controlling. One can also read Peter Pan is a representation of the fleeting dreams children have before deep sleep, imaginings fed by pocket magazines of the day, playing out pirates and Indians? An illustration, At Home in The Nursery, By George Cruickshank, from 1835, depicts children at play with a range of battle inspired toys. War and death are trivialised by play. Even before the story is established, the author makes the distinction that ‘Children have the strangest adventures without being troubled by them’. Peter Pan as a free spirit entices the children to a land of play and adventure. The battle between Peter Pan and Captain Hook suggests a battle between childhood and adulthood, personified by the ever-ticking clock. Peter has ‘no sense of time’. On his parting from Wendy, the children grow up, forgetting Peter. When reminded, Peter does not remember his nemesis, Captain Hook or his companion, Tinkerbell. It seems the battle was only a game, soon forgotten. Much like the adopted trope, ‘it was all a dream’. Neverland never was, only Peter Pan remains. The idea of Peter Pan flying reminds the reader of the prevalence of dreams in which we can fly, that seems part of childhood for many, yet diminish in frequency as we reach adulthood. Peter is innocent and heartless and flies away, because ‘It is only the gay, innocent and heartless that can fly’. Adulthood grounds us. Peter Pan is driven by the notion of self, meeting his own needs and being in the moment, a physical manifestation of freedom, hailing from a none reality of an unobtainable ‘Neverland.’ Ultimately

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