Question 1205308
this is my best shot at what i think is the way to analyze this.
i'm using a two sample z-test.
referenceto that can be found at <a href = "" target = "_blank"></a>


brand A has a mean of 1800 with a standard deviation of 240.
brand B has a mean of 2450 with a standard deviation of 150.
a sample of size 250 is taken from the population of both brands.


the mean of brand A is compared to the mean of brand B using a two sample z-test.
z-score formula is z = (x-m)/s
z is he z-score.
x is the mean of brand A.
m is the mean of brand B.
s is the standard error.


s = sqrt(d1^2/n1 + d2^2/n2)
d1 is the standard deviation of brand A.
d2 is the standard deviation of brand B.
n1 and n2 are the sample size of brand A and brand B.
this is the same at 250.
formula becomes s = sqrt(240^2/250 + 150^2/250) = 17.89972.


z-score formula becomes z = (1800 - 1450) / 17.89972 = 19.55613.
this is a very high z-score, indicating that the mean of brand A is clearly greater than the mean of brand B and that the probability of getting a difference greater than 350 is effectively 0.


based on that, then the probability of getting a mean for brand A that is more than 400 hours greater than the mean for brand B is even less probable, meaning that it is also effectively 0.


here are the results of the two sample t-test using the calculator at <a href = "https://www.statskingdom.com/120MeanNormal2.html" target = "_blank">https://www.statskingdom.com/120MeanNormal2.html</a>


<img src = "http://theo.x10hosting.com/2023/121121.jpg">


<img src = "http://theo.x10hosting.com/2023/121122.jpg">


<img src = "http://theo.x10hosting.com/2023/121123.jpg">