Respuesta :
Answer:
The test statistic value is 15.3.
Step-by-step explanation:
The hypothesis for this test is:
H₀: The average number of homeless people is not increasing, i.e. μ = 42.3.
Hₐ: The average number of homeless people is increasing, i.e. μ > 42.3.
Given:
[tex]\bar x=45.3\\\sigma=6.2\\n=1000[/tex]
As the population standard deviation is provided use a single mean z-test for the hypothesis testing.
The test statistic is:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}=\frac{45.3-42.3}{6.2/\sqrt{1000}}=15.3[/tex]
Thus, the test statistic value is 15.3.
Using the z-distribution, it is found that the test statistic is of z = 15.3.
At the null hypothesis, it is tested if the mean number has not increased, that is, it still is of 42.3, hence:
[tex]H_0: \mu = 42.3[/tex]
At the alternative hypothesis, it is tested if it has increased, that is, the mean is greater than 42.3, hence:
[tex]H_1: \mu > 42.3[/tex]
We have the standard deviation for the population, hence, the z-distribution is used.
The test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The parameters are:
- [tex]\overline{x}[/tex] is the sample mean.
- [tex]\mu[/tex] is the value tested at the null hypothesis.
- [tex]\sigma[/tex] is the standard deviation of the sample.
- n is the sample size.
For this problem, the values of the parameters are:
[tex]\overline{x} = 45.3, \mu = 42.3, \sigma = 6.2, n = 1000[/tex]
Hence:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{45.3 - 42.3}{\frac{6.2}{\sqrt{1000}}}[/tex]
[tex]z = 15.3[/tex]
The test statistic is of z = 15.3.
To learn more about the z-distribution, you can take a look at https://brainly.com/question/16313918
