It is known that the mean diameters of rivets produced by two firms A and B are 53 [7M and 48 respectively, and the standard deviations for 42 rivets produced by firm A, the standard deviation is 2.9mm, while 45 rivets manufactured by firm B, the standard deviation is 3.8mm. Compute the statistic you would use to test whether the
products of firm A have the same as those of firm B and test its significance
To test whether the mean diameters of rivets produced by firms A and B are the same, we can use a two-sample t-test.
The t-statistic for a two-sample t-test is calculated as:
t = (mean of sample A - mean of sample B) / √[(s1^2/n1) + (s2^2/n2)]
Where:
- s1 and s2 are the standard deviations of samples A and B respectively
- n1 and n2 are the sample sizes of samples A and B respectively
Plugging in the given values:
t = (53 - 48) / √[(2.9^2/42) + (3.8^2/45)]
t = 5 / √[(0.1981) + (0.3076)]
t = 5 / √(0.5057)
t = 5 / 0.7113
t = 7.03
To test the significance of this t-statistic, we would compare it to a critical t-value at a given significance level and degrees of freedom. We would then calculate the p-value associated with the t-statistic and compare it to the chosen significance level (e.g., alpha = 0.05).
Based on the result of the test, we would either reject or fail to reject the null hypothesis that the mean diameters of rivets produced by firms A and B are the same.