contestada

A researcher collated data on Americans’ leisure time activities. She found the mean number of hours spent watching television each weekday to be 2.7 hours with a standard deviation of 0.4 hours. Jonathan believes that his football team buddies watch less television than the average American. He gathered data from 15 football teammates and found the mean to be 2.3. Which of the following shows the correct z-statistic for this situation?
-3.87
-0.26
3.23
5.22

Respuesta :

Using the z-distribution, the correct z-statistic for this situation is: z = -3.87.

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 at the null hypothesis, that is, the expected value.
  • [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} = 2.3, \mu = 2.7, \sigma = 0.4, n = 15[/tex]

Hence the z-statistic is found as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{2.3 - 2.7}{\frac{0.4}{\sqrt{15}}}[/tex]

z = -3.87.

More can be learned about the z-distribution at https://brainly.com/question/16313918

#SPJ1

Otras preguntas