Respuesta :
Answer:
There is a significant decrease in the average price homes.
Step-by-step explanation:
Let X represent the prices of homes sold in the U.S. in the past year
given that
[tex]\mu = 220000\\n =81\\\sigma = 36000\\\bar x =210000\\\alpha = 0.05[/tex]
Create hypotheses as
[tex]H_0: \bar x = 220000\\H_a: \bar x <220000[/tex]
(Left tailed test at 5% significance)
Mean difference = -10000
Std error of mean = [tex]\frac{\sigma}{\sqrt{n} } \\=4000[/tex]
Since population std deviation is known, we can do z test
Z = mean diff/std error = -2.50
p value = 0.00621
Since p <0.05 we reject null hypothesis.
There is a significant decrease in the average price homes.
Here, P < 0.05 then reject the null hypothesis and accept the alternate hypothesis.
There has been a significant decrease in the average price homes.
Given that,
The average price of homes sold in the U.S. in the past year was $220,000.
A random sample of 81 homes sold this year showed an average price of $210,000.
The standard deviation of the population is $36,000.
We have to determine,
At level of significance (a) 0.05, conduct the hypothesis test to determine if there has been a significant decrease in the average price homes.
According to the question,
The hypothesis test to determine if there has been a significant decrease in the average price homes.
Let, x represent the prices of homes sold in the U.S. in the past year.
The hypothesis test is determined by formula,
[tex]Z_s_t_a_t = \dfrac{x_1-\mu}{\frac{\sigma} {\sqrt{n}}}[/tex]
Where, Population mean, μ = $220,000 ,
Sample mean,[tex]x_1[/tex] = $210,000 , Sample size, n = 81 ,
Significance level, α = 0.051 ,
Population standard deviation, σ = $36,000.
The null and the alternate hypothesis,
[tex]H_0 ;\mu = 220000 dollars\\\\H_a; \mu<210000[/tex]
Substitute all the values in the formula,
[tex]Z_s_t_a_t = \dfrac{210000-220000}{\frac{36000} {\sqrt{81}}}\\\\Z_s_t_a_t = \dfrac{-100000}{\frac{\36000} {9}}\\\\Z_s_t_a_t = \dfrac{-10000}{4000}\\\\Z_s_t_a_t = -2.5[/tex]
The p-value from the z-table,
P-value = 0.00621
Here, P-value < Significance level
Since, P < 0.05 then reject the null hypothesis and accept the alternate hypothesis.
Hence, There has been a significant decrease in the average price homes.
To know more about Hypothesis click the link given below.
https://brainly.com/question/14965054
