Respuesta :
Using the z-distribution, it is found that since the p-value is less than 0.05, there is evidence to support the claim that the average cost of private universities are decreasing.
What are the hypothesis tested?
At the null hypothesis, it is tested if the average cost is still of $50,000, that is:
[tex]H_0: \mu = 50000[/tex]
At the alternative hypothesis, it is tested if the average cost is decreasing, that is:
[tex]H_1: \mu < 50000[/tex]
What is the test statistic?
The test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
- [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 population.
- n is the sample size.
The parameters for this problem are:
[tex]\overline{x} = 49450, \mu = 50000, \sigma = 2500, n = 100[/tex]
Hence:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{49450 - 50000}{\frac{2500}{\sqrt{100}}}[/tex]
z = -2.2.
What is the p-value and the conclusion?
Using a z-distribution calculator, for a left-tailed test, as we are testing if the mean is less than a value, with z = -2.2, the p-value is of 0.0139.
Since the p-value is less than 0.05, there is evidence to support the claim that the average cost of private universities are decreasing.
More can be learned about the z-distribution at https://brainly.com/question/16313918
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