Answer:
1
The claim is that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial
2
The kind of test to use is a t -test because a t -test is used to check if there is a difference between means of a population
3
![t = 3.054](https://tex.z-dn.net/?f=t%20%20%3D%20%203.054)
4
The p-value is ![p-value = P(Z > 3.054) = 0.0011291](https://tex.z-dn.net/?f=p-value%20%20%3D%20%20P%28Z%20%3E%20%203.054%29%20%3D%200.0011291)
5
The conclusion is
There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial
The test statistics is
Step-by-step explanation:
From the question we are told that
The first sample size is ![n_1 = 51](https://tex.z-dn.net/?f=n_1%20%20%3D%20%2051)
The first sample mean is ![\mu_1 = 36](https://tex.z-dn.net/?f=%5Cmu_1%20%20%3D%20%2036)
The second sample size is ![n_2 = 41](https://tex.z-dn.net/?f=n_2%20%20%3D%20%2041)
The second sample size is ![\mu_2 = 25](https://tex.z-dn.net/?f=%5Cmu_2%20%20%3D%20%2025)
The first standard deviation is ![\sigma _1 = 21.4 \ g](https://tex.z-dn.net/?f=%5Csigma%20_1%20%20%3D%20%2021.4%20%5C%20%20g)
The second standard deviation is ![\sigma _2 = 12.8 \ g](https://tex.z-dn.net/?f=%5Csigma%20_2%20%20%3D%20%2012.8%20%5C%20%20g)
The level of significance is ![\alpha = 0.05](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%200.05)
The null hypothesis is ![H_o : \mu_1 = \mu_ 2](https://tex.z-dn.net/?f=H_o%20%20%3A%20%20%5Cmu_1%20%3D%20%5Cmu_%202)
The alternative hypothesis is ![H_a : \mu_1 > \mu_2](https://tex.z-dn.net/?f=H_a%20%3A%20%20%5Cmu_1%20%3E%20%5Cmu_2)
Generally the test statistics is mathematically represented as
![t = \frac{\= x_1 - \= x_2}{ \sqrt{ \frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} } }](https://tex.z-dn.net/?f=t%20%20%3D%20%20%5Cfrac%7B%5C%3D%20x_1%20-%20%5C%3D%20x_2%7D%7B%20%5Csqrt%7B%20%5Cfrac%7Bs_1%5E2%7D%7Bn_1%7D%20%20%2B%20%5Cfrac%7Bs_2%5E2%7D%7Bn_2%7D%20%20%7D%20%7D)
=> ![t = \frac{ 36 - 25}{ \sqrt{ \frac{ 21.4^2}{51} + \frac{ 12.8^2}{41} } }](https://tex.z-dn.net/?f=t%20%20%3D%20%20%5Cfrac%7B%2036%20-%2025%7D%7B%20%5Csqrt%7B%20%5Cfrac%7B%2021.4%5E2%7D%7B51%7D%20%20%2B%20%5Cfrac%7B%2012.8%5E2%7D%7B41%7D%20%20%7D%20%7D)
=> ![t = 3.054](https://tex.z-dn.net/?f=t%20%20%3D%20%203.054)
The p-value is mathematically represented as
![p-value = P(Z > 3.054)](https://tex.z-dn.net/?f=p-value%20%20%3D%20%20P%28Z%20%3E%20%203.054%29)
Generally from the z table
![P(Z > 3.054) = 0.0011291](https://tex.z-dn.net/?f=P%28Z%20%3E%20%203.054%29%20%3D%20%200.0011291)
=> ![p-value = P(Z > 3.054) = 0.0011291](https://tex.z-dn.net/?f=p-value%20%20%3D%20%20P%28Z%20%3E%20%203.054%29%20%3D%200.0011291)
From the values obtained we see that
so the null hypothesis is rejected
Thus the conclusion is
There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial