(a) State the null and alternative hypothesis. (b) Calculate the approximate tes
ID: 3221348 • Letter: #
Question
(a) State the null and alternative hypothesis.
(b) Calculate the approximate test-statistic using the normal approximation to binomial.
(c) Calculate the p-value associated with the teststatistic in (b).
(d) Use R to calculate the exact p-value for the hypothesis test. How large of a difference was there?
(e) State your conclusion in terms of the problem, if = 0.05.
(f) Using R, calculate the exact 90% confidence interval for the true median.
(g) Using the normal approximation to the binomial distribution, calculate the lower and upper bound for a 90% confidence interval for the true median.
(h) Which interval is narrower, and why?
The weights for a particular breed of chicken follow in pounds (in increasing order by row): 3.75 3.78 3.84 3.84 3.88 3.92 3.93 3.93 3.94 3.94 3.96 3.96 3.96 3.98 3.99 4.02 4.02 4.03 4.06 4.06 4.09 4.10 4.12 4.17 Note, this data can be found under the Dataset folder on Canvas, as chicken.csv. The breeder claims that the median weight for the chickens is 4 lbs.Explanation / Answer
Answer to part a)
The claim is that median weight is 4lbs
Thus null hypothesis: Ho: M = 4lbs
Alternate hypothesis : H1: 4lbs
.
Answer to part b)
15 values < 4
9 values > 4
.
Since there are total 24 values : there must be :
12 values < 4
12 values > 4
.
Thus chi square = (15 - 12)^2/12 + (9-12)^2/12 = 162/12 = 1.5
df = 2
Thus the test statistic (Chi Square) = 1.5
.
Answer to part c)
the P value for chi square 1.5 and df = 2 is :
P value = 0.4724
.
Answer to part d)
Form R we get the P value = 0.4724, which is exactly the same as I got with the help of online P vlaue calculator
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