Question

A six-sided die is rolled 120 times. Fill in the expected frequency column. Then, conduct a hypothesis test at the 5% level to determine if the die is fair. The data below are the result of the 120 rolls. (Enter exact numbers as integers, fractions, or decimals.)
Face Value Frequency Expected Frequency
1 14 ?
2 33 ?
3 15 ?
4 14 ?
5 30 ?
6 14 ?

Required:
a. State the null hypothesis.
b. State the alternative hypothesis.
c. What are the degrees of freedom?

Answer 1

Answer:

Die is not fair given that  Pvalue< 0.05, hence we reject Null hypothesis

a) H0: Die = fair

b) Ha : Die ≠ fair

c) df = 5

Step-by-step explanation:

The expected frequency of every face values = 20

a) state Null hypothesis

H0: Die = fair

b) Alternate Hypothesis

Ha : Die ≠ fair

c) degree of freedom

df = ( n - 1 )

   = ( 6 - 1 ) = 5

n = sample size ( number of faces a die has )

Note : After conducting hypothesis test

Pvalue ≈  0.0026

test statistic ≈ 18.30

Hence we can conclude that die is not fair given that  Pvalue < 0.05, hence we reject Null hypothesis