Answer:
The researcher can conclude that the mean is not 82. i.e. the people will have different accuracy than the general population.
Step-by-step explanation:
mean, [tex]\mu = 82[/tex]
Variance, v = 20
Sample size, n = 50
Standard deviation, [tex]\sigma = \sqrt{20} = 4.4721[/tex]
Sample mean, [tex]\bar{X} = 78[/tex]
Level of significance, [tex]\alpha = 0.05[/tex]
Null hypothesis, [tex]H_o: \mu = 82\\[/tex]
Alternative hypothesis, [tex]H_a: \mu \neq 82[/tex]
Calculate the test statistics:
[tex]z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n} } \\\\z = \frac{78 - 82}{4.4721\sqrt{50} }\\\\z = - 6.32[/tex]
Get the critical value of z at 5% significant level:
[tex]z_{crit} = \pm 1.96[/tex]
Since the test statistics is less than the critical values of z, the null hypothesis is rejected.
