Armando thinks that he has a special relationship with
the number 4. In particular, Armando thinks that he would roll a 4
with a fair 6-sided die more often than you'd expect by chance
alone. Suppose pp is the true proportion of the time Armando will
roll a 4.
(a) State the null and alternative hypotheses for
testing Armando's claim. (Type the symbol "p" for the population
proportion, whichever symbols you need of "<", ">", "=", "not
=" and express any values as a fraction e.g. p = 1/3)
H0=
Ha=
(b) Now suppose Armando makes n = 38 rolls, and a 4
comes up 8 times out of the 38 rolls. Determine the P-value of the
test, giving your answer to 4 decimal places. Please use 3 decimal
places in your test statistic.
P-value =
(c) Answer the question: Does this sample provide
evidence at the 5 percent level that Armando rolls a 4 more often
than you'd expect?
(Type: Yes or No)
Answer:
a)
Given,
p = 1/6 = 0.1667
Ho : p = 0.1667
Ha : p > 0.1667
sample proportion p^ = x/n = 8/38 = 0.2105
test statistic z = (p^ - p)/sqrt(p(1-p)/n)
substitute values
= (0.2105 - 0.1667)/sqrt(0.1667(1 -0.1667)/38)
z = 0.7244
b)
P value = P(z > 0.7244)
= 0.2344101 [since from z table]
= 0.23444
c)
Here p value > alpha, so we fail to reject Ho.
So we don't have sufficient evidence.
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