Respuesta :
Answer:
The population mean is not different from 14.5.
Step-by-step explanation:
The two tailed hypothesis to test whether the population mean is 14.5 or not is:
H₀: The population mean is 14.5, i.e. μ = 14.5.
Hₐ: The population mean is different from 14.5, i.e. μ ≠ 14.5.
The information provided is:
[tex]\bar x=15\\s=2\\\alpha =0.05[/tex]
As the population standard deviation is not provided use a t-test for single mean.
The test statistic is:
[tex]t=\frac{\bar x-\mu}{s/\sqrt{n}} =\frac{15-14.5}{2/\sqrt{16}}=1[/tex]
The test statistic value is 1.
Decision rule:
The critical value of t for α = 0.05 and degrees of freedom, (n - 1) = 15 is:
[tex]t_{0.05/2, 15}=\pm 2.131[/tex]
If the test statistic value lies outside the range (-2.131, 2.131) then the null hypothesis will be rejected.
The test statistic value is 1.
This value lies in the range (-2.131, 2.131).
Thus, the null hypothesis was failed to be rejected at 5% level of significance.
Conclusion:
As the null hypothesis was not rejected it can be concluded that the population mean is not different from 14.5.
