Question

1. A casino wants to see if a six-sided die is fair. They perform an experiment in which they roll the die 100 times and count the number of times the result is a 3. (a) Is this a one or two-sided test? Explain your answer in a complete sentence. (b) Set up the hypotheses for this test both in words and in terms the parameter p which denotes the theoretical probability for getting a roll of the die giving a 3. (c) Out of 100 rolls, they find that 20 result in the number 3 being rolled. What is the observed test statistic? Use appropriate notation for your answer. (d) What is the nulll distribution for this example? (e) Calculate the P-value of the observed test statistic using the null distribution you identified in the previous part. (f) Interpret the practical meaning of the P-value. For example write out a complete sentence that explains what the P -value is measuring.

Answer 1

Answer:

Given,

a)

This a two sided test as we need to locate that six-sided bite the dust is reasonable or not. That is the reason we will utilize two sided test.

b)

Here invalid speculation is that the hypothetical likelihood for getting a move of the bite the dust giving a 3 is 1/6.

Ho : p = 1/6

Elective speculation is that the hypothetical likelihood for getting a move of the kick the bucket giving a 3 isn't equivalent to 1/6.

Ha : p != 1/6

c)

Here watched test measurement = p^ = x/n

= 20/100

= 0.2

d)

Here invalid circulation is ordinary with expected extent = 1/6

standard deviation = sqrt (pq/n)

= (1/6 * 5/6 * 1/100)

= 0.0373

Test statistic

z = (p^ - p)/s

z = (0.2 - 1/6)/0.0373

z = 0.8944

e)

p - esteem = 2 * P(Z > 0.8944)

= 2*0.185554 [since from z table]

= 0.3711

f)

Here down to earth importance of the p - esteem is that if the six sided pass on is reasonable than likelihood of getting three, 20 or more is 0.3711 that is more noteworthy than 0.05.

so we would neglect to dismiss the invalid theory and reason that six sided dice is reasonable.