Question

You wish to test the following claim (HaHa) at a significance level of α=0.02α0.02.

      Ho:p=0.88Hop0.88
      Ha:p<0.88Hap0.88

You obtain a sample of size n=553n553 in which there are 483 successful observations. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

Answer 1

Solution :

Given that,

n = 553

x = 483

= x / n = 483/553

= 0.87

Hypothesis:

Ho:p = 0.88

Ha:p < 0.88

Test Statistic:

Z =   - P / ( ((P * (1 - P)) / n)

Z = 0.87 -0.88 / ( ((0.88* 0.12) / 553)

Z = - 0.724

Z = - 0.724

P- value = 0.2345

If P-value <   = 0.02 , then we reject null hupothesis.

P- value = 0.2345 > 0.02 fail to reject H0

There is not enough evidence to support the claim.