Question

John wants to test whether a new die that he has is truly random. He rolls the die 80 times and measures the number of times the die falls on an even number. He measures an even number 46 times. John conducts a one-proportion hypothesis at the 5% significance level, to test whether the true proportion of even numbers is different from 50%. For this test: H0:p=0.5; Ha:p≠0.5, which is a two-tailed test. The test results are: z0=1.342, p-value =0.180 Which of the following are appropriate conclusions for this hypothesis test? Select all that apply. Select all that apply: We reject H0.

We fail to reject H0.

At the 5% significance level, the data provide sufficient evidence to conclude the true proportion is different than 50%.

At the 5% significance level, the data do not provide sufficient evidence to conclude the true proportion is different than 50%.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.50

Ha : p 0.50

n = 80

x = 46

= x / n = 46 / 80 = 0.575

P0 = 0.50

1 - P0 = 1 - 0.50 =0.50

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.575 - 0.50 / [0.50*0.50 / 80 ]

= 1.342

P(z > 1.342 ) = 1 - P(z < 1.342 ) = 1 -0.9102

P-value = 2 * 0.0898 = 0.180

= 0.05

P-value >

0.180 > 0.05

Fail to reject the null hypothesis .

There is not provide sufficient evidence to conclude the true proportion is different than 50%.