Question

The national mean sales price for a new one-family home is $181,900. A sample of 40 one-family homes in the south showed a sample mean of $166,400 and a sample standard deviation of $ 33,500.
Required:
a. Formulate the null and alternative hypothesis for this problem so the sample data support the conclusion that the population mean sales prices for new one-family homes in the South is less expensive than the national mean of $181,900.
b. What is the value of the test statistic?
c. What is the p-value?
d. At α = 0,01 what is your conclusion?

Answer 1

Answer:

a

The  null hypothesis is  $\mu = \ 181,900$

The alternative hypothesis is  $\mu < \ 181.900$

b

$t = -2.92$

c

$p-value = 0.0016948$

d

There no sufficient evidence to support the conclusion that the population mean sales prices for new one-family homes in the South is less expensive than the national mean of $181,900

Step-by-step explanation:

From the question we are told that

   The  population mean is  $\mu = \ 181, 900$

    The  sample size is  $n = 40$

    The  sample  mean is  $\= x = \ 166,400$

      The  sample  standard deviation is $s= \ 33, 500$

The  null hypothesis is  $\mu = \ 181,900$

The alternative hypothesis is  $\mu < \ 181.900$

 

Generally the test statistics is mathematically represented as

      $t = \frac{ \= x - \mu }{ \frac{s}{\sqrt{n} } }$

=>    $t = \frac{ 166400 - 181900 }{ \frac{33500}{\sqrt{40} } }$

=>    $t = -2.92$

Generally the p-value is obtain from the z-table  the value is  

      $p-value = P(Z < t ) = P(Z < -2.93) = 0.0016948$

=>    $p-value = 0.0016948$

From the calculation we see that  

     $p-value > \alpha$  hence we fail to reject the null hypothesis

Thus there no sufficient evidence to support the conclusion that the population mean sales prices for new one-family homes in the South is less expensive than the national mean of $181,900