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Sagot :
Using the z-distribution, the p-value for the test is of 0.0040.
What is the test statistic for the z-distribution?
The test statistic is given by:
[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.
- [tex]\sigma[/tex] is the standard deviation of the population.
- n is the sample size.
For this problem, the parameters are given as follows:
[tex]\overline{x} = 33.8, \mu = 32, \sigma = 4.3, n = 40[/tex]
Hence the value of the test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
z = (33.8 - 32)/(4.3/sqrt(40))
z = 2.65.
What is the p-value?
Using a z-distribution calculator, with z = 2.65 and a right-tailed test, as we are testing if the mean is greater than a value, the p-value is of 0.0040.
More can be learned about the z-distribution at https://brainly.com/question/16313918
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