Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .10 significance level. Let p_M and p_F be the proportion of Men and Women who own cats respectively. Based on a sample of 80 men, 40% owned cats
Based on a sample of 80 women, 51% owned cats
What is the test statistic and the critical value? Reject or Fail to Reject Null hypothesis?

 The  test statistics is

  The critical value is  

   The null hypothesis is rejected

Step-by-step explanation:

From the question we are told that

   The sample size  for men is  

    The sample  proportion of men that own a cat is  

     The  sample  size for  women is

     The sample  proportion of women that own a cat is  

     The level of significance is  

   The  null hypothesis is  

    The alternative hypothesis is  

Generally the test statistic is mathematically represented as

=>  

=>  

The critical value of    from the normal distribution table is

The p-value  is obtained from the z-table ,the value is  

=>    

Given that the then we reject the null hypothesis