Question

A housing policy research group reported that the proportion of homeowners in the U.S. who struggle to make monthly mortgage payments is 0.29, or 29%. A real estate company is interested in examining this claim in a particular state that has experienced recent economic hardships Refer to the information above regarding the survey of homeowners with mortgages. The survey found that in a sample of 451 randomly selected homeowners, 183 reported having difficulty paying their mortgages each month. If a hypothesis test were to be conducted to determine if the problem is worse in this particular state, which of the following would be the correct value of the test statistic? Choose the closest value, taking all calculations to four decimal places.

a) 5.42
b) 0.45
c) 0.36
d) 18.99
e) 0.26

Answer 1

The option is A

Explanation:

From the question we are told that

The population proportion is
`p =  0.29`

The sample size is n = 451

The number that was having difficulty is k = 183

Generally the sample proportion is mathematically represented as

`\^ {p}  =  (k)/(n)`

=>
`\^ {p}  =  (183)/(451)`

=>
`\^ {p}  =   0.4058`

Generally the test statistics is mathematically represented as

`t = \frac{ \^ {p} -  p }{ \sqrt{(p (1-p))/(n) } }`

=>
`t = \frac{0.4058 -  0.29 }{ \sqrt{(0.29 (1-0.29))/(451) } }`

=>
`t =  5.42`