Answer:
a
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to show that there is a difference between the performances of these two models
b
The 95% confidence interval is
Step-by-step explanation:
From the question we are told that
The sample size is n = 36
The first sample mean is ![\= x_1 = 11.4](https://tex.z-dn.net/?f=%5C%3D%20x_1%20%20%20%3D%20%2011.4)
The first standard deviation is
The second sample mean is ![\= x_2 = 9.9](https://tex.z-dn.net/?f=%5C%3D%20x_2%20%3D%20%209.9)
The second standard deviation is ![s_2 = 3.0](https://tex.z-dn.net/?f=s_2%20%3D%20%203.0)
The level of significance is ![\alpha = 0.05](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%200.05)
The null hypothesis is ![H_o : \mu_1 - \mu_2 = 0](https://tex.z-dn.net/?f=H_o%20%20%3A%20%20%5Cmu_1%20-%20%5Cmu_2%20%3D%200)
The alternative hypothesis is ![H_a : \mu_1 - \mu_2 \ne 0](https://tex.z-dn.net/?f=H_a%20%3A%20%20%5Cmu_1%20-%20%5Cmu_2%20%5Cne%200)
Generally the test statistics is mathematically represented as
![z = \frac{ (\= x_1 - \= x_2 ) - (\mu_1 - \mu_2 ) }{ \sqrt{ \frac{s_1^2 }{n} + \frac{s_2^2 }{ n} } }](https://tex.z-dn.net/?f=z%20%3D%20%20%5Cfrac%7B%20%28%5C%3D%20x_1%20-%20%5C%3D%20x_2%20%29%20-%20%28%5Cmu_1%20-%20%5Cmu_2%20%29%20%7D%7B%20%5Csqrt%7B%20%5Cfrac%7Bs_1%5E2%20%7D%7Bn%7D%20%2B%20%5Cfrac%7Bs_2%5E2%20%7D%7B%20n%7D%20%20%7D%20%7D)
=> ![z = \frac{ ( 11.4 - 9.9) - 0 }{ \sqrt{ \frac{2.5^2 }{36} + \frac{ 3^2 }{36 } } }](https://tex.z-dn.net/?f=z%20%3D%20%20%5Cfrac%7B%20%28%2011.4%20%20-%209.9%29%20-%200%20%20%7D%7B%20%5Csqrt%7B%20%5Cfrac%7B2.5%5E2%20%7D%7B36%7D%20%2B%20%5Cfrac%7B%203%5E2%20%7D%7B36%20%7D%20%20%7D%20%7D)
=> ![z = 2.3](https://tex.z-dn.net/?f=z%20%3D%202.3)
From the z table the area under the normal curve to the left corresponding to 2.3 is
![P( Z > 2.3 ) = 0.010724](https://tex.z-dn.net/?f=P%28%20Z%20%3E%20%202.3%20%29%20%3D%20%200.010724)
Generally the p-value is mathematically represented as
![p-value = 2 * P( Z > 2.3 )](https://tex.z-dn.net/?f=p-value%20%3D%20%202%20%2A%20P%28%20Z%20%3E%20%202.3%20%29)
=> ![p-value = 2 * 0.010724](https://tex.z-dn.net/?f=p-value%20%20%3D%20%202%20%2A%200.010724)
=> ![p-value = 0.02](https://tex.z-dn.net/?f=p-value%20%20%3D%20%200.02)
From the value obtained we see that
hence
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to show that there is a difference between the performances of these two models
Considering question b
From the question we are told the confidence level is 95% , hence the level of significance is
=>
Generally from the normal distribution table the critical value of
is
Generally the margin of error is mathematically represented as
=>
=>
Generally 95% confidence interval is mathematically represented as
=>
=>