Answer :
To find the point estimate for the true difference between the given population means of Soap Bar A and Soap Bar B, we need to calculate the mean weight for each soap and then find the difference between these two means.
Step-by-step Calculation:
Calculate the Mean for Soap Bar A:
The weights for Soap Bar A are: 123, 124, 122, 123, 123, 125, 123, 124, 122, 124, 123.The mean ([tex]\bar{x}_A[/tex]) can be calculated as:
[tex]\bar{x}_A = \frac{123 + 124 + 122 + 123 + 123 + 125 + 123 + 124 + 122 + 124 + 123}{11}[/tex]
[tex]\bar{x}_A = \frac{1336}{11} \approx 121.454545[/tex]Calculate the Mean for Soap Bar B:
The weights for Soap Bar B are: 124, 121, 122, 123, 121, 121, 123, 126, 126, 120, 122, 122, 122.The mean ([tex]\bar{x}_B[/tex]) can be calculated as:
[tex]\bar{x}_B = \frac{124 + 121 + 122 + 123 + 121 + 121 + 123 + 126 + 126 + 120 + 122 + 122 + 122}{13}[/tex]
[tex]\bar{x}_B = \frac{1473}{13} \approx 122.000000[/tex]Find the Difference Between the Means:
Now, subtract the mean weight of Soap Bar B from the mean weight of Soap Bar A to get the point estimate of the difference:
[tex]\bar{x}_A - \bar{x}_B = 121.454545 - 122.000000 = -0.545455[/tex]Round the Difference to Six Decimal Places:
So, the point estimate for the true difference between the populations means is approximately [tex]-0.545455[/tex].
Therefore, the point estimate indicates that, on average, Soap Bar A is approximately 0.545455 grams lighter than Soap Bar B.
