Statistics- What is the estimate of the true difference between the proportions

QUESTION

Word Problems

1)
(6 points total) A
consumer advocate agency is concerned about reported failures of two brands of
MP3 players, which we will label Brand A and Brand B. In a random sample of 197 Brand A players, 33
units failed within 1 year of purchase.
Of the random sample of 290 Brand B players, 25 units were reported to
have failed within the first year following purchase. The agency is interested in the difference
between the population proportions,.0/msohtmlclip1/01/clip_image002.gif”>, for the two brands.
a. What
is the estimate of the true difference between the proportions (D), and the
standard error of the estimate (.0/msohtmlclip1/01/clip_image004.gif”>)?
b.
What is the 99% confidence interval
estimate of the true difference,.0/msohtmlclip1/01/clip_image002.gif”>?

2)
(18 points total) A study was performed to examine the personal goals of children in
grades 4, 5, and 6. A random sample of
students was selected from each of the grades 4, 5, and 6 from schools New York. The students received a questionnaire
regarding achieving personal goals. They
were asked what they would most like to do at school: make good grades, be good
at sports, or be popular. Results are
presented by the gender of the child in the table below:

Goal

Boys

Girls

Make good grades

96

295

Be popular

32

45

Be good in sports

94

45

a.
(2 points) What is the marginal distribution of gender? Of personal goals? Summarize in a table and show work.
b.
(3 points)What is the conditional
distribution of personal goals for boys? For girls? Summarize in a table and show work.
c.
(3 points)Briefly compare these
conditional distributions. Does there
appear to be an association between gender and personal goals? Briefly explain.
d.
(7 points)Now, use a chi-square test to
test the association between gender and personal goals. State the null and alternative
hypotheses. Compute the observed test
statistic and infer the p-value
(assume the conventional .05 significance level). Show all work.
e.
(3 points total) What can you conclude based on your work in part (d)? Make sure you
clearly indicate what you are comparing your test statistic and inferred p-value against.

ANSWER:

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