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------------------------------------------------ Find the point estimate for the true difference between the given population means. Round your answer to six decimal places.

Weights (in grams) of Soap Bar A: 123, 124, 122, 123, 123, 125, 123, 124, 122, 124, 123

Weights (in grams) of Soap Bar B: 124, 121, 122, 123, 121, 121, 123, 126, 126, 120, 122, 122, 122

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:

  1. 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]

  2. 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]

  3. 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]

  4. 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.