Answer:
a
The null hypothesis is [tex]\mu = \$181,900[/tex]
The alternative hypothesis is [tex]\mu < \$ 181.900[/tex]
b
[tex]t = -2.92[/tex]
c
[tex]p-value = 0.0016948[/tex]
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 [tex]\mu = \$ 181, 900[/tex]
The sample size is [tex]n = 40[/tex]
The sample mean is [tex]\= x = \$ 166,400[/tex]
The sample standard deviation is [tex]s= \$ 33, 500[/tex]
The null hypothesis is [tex]\mu = \$181,900[/tex]
The alternative hypothesis is [tex]\mu < \$ 181.900[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \= x - \mu }{ \frac{s}{\sqrt{n} } }[/tex]
=> [tex]t = \frac{ 166400 - 181900 }{ \frac{33500}{\sqrt{40} } }[/tex]
=> [tex]t = -2.92[/tex]
Generally the p-value is obtain from the z-table the value is
[tex]p-value = P(Z < t ) = P(Z < -2.93) = 0.0016948[/tex]
=> [tex]p-value = 0.0016948[/tex]
From the calculation we see that
[tex]p-value > \alpha[/tex] 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
