Question

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 1

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.