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

The correct option is a

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 \\e 0.3`

The test statistics is mathematically evaluated as

`t = (\r p - p )/( (√( p (1- p )) )/(n) )`

substituting values

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

`t = 8.446`