Answer:
Step-by-step explanation:
Here are the missing values;
Mean μ = 15.5 minutes
Standard deviation = 1.7 minutes
A Random sample of 90 completion
The sample mean = 15.4 minutes
Level of significance = 0.1
Then the following analysis can be made on the above study.
Firstly, the null hypothesis is ![\mathbf{H_o : \mu = 15.5}](https://tex.z-dn.net/?f=%5Cmathbf%7BH_o%20%3A%20%5Cmu%20%3D%2015.5%7D)
the alternative hypothesis is
Since, the value is less than, then this is a one-tailed test.
The Z test statistics can be computed as:
![Z = \dfrac{ \overline x - \mu }{\dfrac{\sigma}{\sqrt{n}} } \ \ \sim \ \ N(0.1)](https://tex.z-dn.net/?f=Z%20%3D%20%5Cdfrac%7B%20%5Coverline%20x%20-%20%5Cmu%20%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%20%20%7D%20%20%5C%20%5C%20%20%5Csim%20%20%5C%20%5C%20%20N%280.1%29)
![Z = \dfrac{ 15.4-15.5 }{\dfrac{1.7}{\sqrt{90}} }](https://tex.z-dn.net/?f=Z%20%3D%20%5Cdfrac%7B%2015.4-15.5%20%7D%7B%5Cdfrac%7B1.7%7D%7B%5Csqrt%7B90%7D%7D%20%20%7D)
![Z = \dfrac{ -0.1 }{\dfrac{1.7}{ 9.4868} }](https://tex.z-dn.net/?f=Z%20%3D%20%5Cdfrac%7B%20-0.1%20%7D%7B%5Cdfrac%7B1.7%7D%7B%209.4868%7D%20%20%7D)
Z = −0.560
The critical value of Z at 0.1 level of significance is:
![Z_{0.1} = -1.28](https://tex.z-dn.net/?f=Z_%7B0.1%7D%20%3D%20-1.28)
Decision Rule: We fail to reject the null hypothesis sInce -0.560 > -1.28
Conclusion: NO, there is no evidence to support the claim that the mean completion time has decreased. We conclude that the mean completion time remains at 15.5 minutes.