Answer: A. -4.47
Step-by-step explanation:
As per given , we have
[tex]H_0: \mu\geq7\\\\ H_a: \mu<7[/tex]
sample size : n= 1264
Sample mean : [tex]\overline{x}=6.02[/tex]
Sample standard deviation : s=7.80
Since the population standard deviation is unknown , so we use t-test.
Test statistic : [tex]t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}[/tex]
[tex]t=\dfrac{6.02-7}{\dfrac{7.80}{\sqrt{1264}}}[/tex]
Simplify , we get
[tex]t=-4.46688745075\approx-4.47[/tex]
Hence, the test statistic : t= -4.47
Using the t-distribution, as we have the standard deviation for the sample, it is found that the test statistic is given by:
A. -4.47
At the null hypothesis, it is tested if they spend 7 hours a week answering their email, that is:
[tex]H_0: \mu = 7[/tex]
At the alternative hypothesis, it is tested if they spend less than 7 hours, that is:
[tex]H_1: \mu < 7[/tex].
The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
In this problem, the parameters are given as follows:
[tex]\overline{x} = 6.02, \mu = 7, s = 7.8, n = 1264[/tex]
Hence, the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{6.02 - 7}{\frac{7.8}{\sqrt{1264}}}[/tex]
[tex]t = -4.47[/tex]
Thus, option A is correct.
To learn more about the t-distribution, you can check https://brainly.com/question/16313918
