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Sagot :
Using the t-distribution, it is found that the value of the test statistic is t = -87.3.
At the null hypothesis, it is tested if the mean is of 2,463 square feet, that is:
[tex]H_0: \mu = 2463[/tex]
At the alternative hypothesis, it is tested if the mean is smaller, that is:
[tex]H_1: \mu < 2463[/tex].
We have the standard deviation for the sample, hence, the t-distribution is used to solve this question.
The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\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.
- s is the standard deviation of the sample.
- n is the sample size.
The values of the parameters are: [tex]\overline{x} = 1640, \mu = 2463, s = 66, n = 49[/tex].
Hence, the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{1640 - 2463}{\frac{66}{\sqrt{49}}}[/tex]
[tex]t = -87.3[/tex]
To learn more about the t-distribution, you can take a look at https://brainly.com/question/25819230
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