A large software development firm recently relocated its facilities. Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities. They believe that the firm's professionals volunteer an average of more than 15 hours per month. If this is not the case, they will institute an incentive program to increase community involvement. A random sample of 24 professionals yields a mean of 16.6 hours and a standard deviation of 2.22 hours. The correct value of the test statistic for the appropriate hypothesis test is

Question

contestada

Respuesta :

JeanaShupp JeanaShupp · Answer 1 · 2019-07-10T07:40:20+02:00

Answer: 3.5308

Step-by-step explanation:

Claim : The firm's professionals volunteer an average of more than 15 hours per month.

i.e. [tex]\mu>15[/tex]

Null hypothesis : [tex]H_0:\mu\leq15[/tex]

Alternative hypothesis : [tex]H_1:\mu>15[/tex]

Sample size : [tex]n=24[/tex]

The sample mean : [tex]\overline{x}=16.6\text{ hours}[/tex]

Sample standard deviation : [tex]\sigma=2.22\text{ hours}[/tex]

The test-statistics for the population mean is given by :-

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

i.e. [tex]z=\dfrac{16.6-15}{\dfrac{2.22}{\sqrt{24}}}=3.5307960256\approx3.5308[/tex]

Hence, the correct value of the test statistic for the appropriate hypothesis test is 3.5308.