Question

You wish to test the following claim a significance level of α=0.005.

Ho:p=0.71
Ha:p≠0.71

You obtain a sample of size n=164 in which there are 111 successful observations.

1. What is the test statistic for this sample?
   
   test statistic =  Round to 3 decimal places.
   
2. What is the p-value for this sample?
   
   P-value =  Use Technology Round to 4 decimal places.
   
3. The p-value is...
   • less than (or equal to) αα
   • greater than αα
   
   
4. This test statistic leads to a decision to...
   • reject the null
   • accept the null
   • fail to reject the null
   
   
5. As such, the final conclusion is that...
   • There is sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.71.
   • There is not sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.71.
   • The sample data support the claim that the population proportion is not equal to 0.71.
   • There is not sufficient sample evidence to support the claim that the population proportion is not equal to 0.71.

Answer 1

Ho:p=0.71
Ha:p≠0.71

Sample size , n=164

x = 111

= 111/ 164 = 0.6768

(a) Test statistics, z= = = -0.947

(b) P-Value = 2 [ P( z > 0.95) ] = 2 [ 1- P( z< 0.95)] = 2 [ 1- 0.82894] = 0.3421

greater than α  

(c)This test statistic leads to a decision to..-

Fail to reject the null hypothesis.

(d) The final conclusion is-

  There is sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.71.