Question

A hypothesis test is to be performed for a population proportion. For the given sample data and null hypothesis, compute the value of the test statistic, Z.
415 people were asked if they were satisfied with their jobs. 49% said they were. H0: p= 0.3

a. 8.446
b. 2.612
c. 0.415
d. 4.125

Answer 1

Answer:

The correct option is a

Step-by-step explanation:

From the question we are told that

    The sample size is n =  415

    The sample proportion is  $\r p = 0.49$

Now

     The null hypothesis is  $H_o : p = 0.3$

     The alternative hypothesis is $H_a : p \ne 0.3$

The test statistics is mathematically evaluated as

      $t = \frac{\r p - p }{ \frac{\sqrt{ p (1- p )} }{n} }$

substituting values

      $t = \frac{0.49 - 0.3 }{ \sqrt{ \frac{0.3 (1- 0.3 ) }{415} }}$

     $t = 8.446$