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Answer :
To find the point estimate for the true difference between the given population means, we'll calculate the sample mean for each group of smartphone weights, then subtract those means.
Step 1: Calculate the Sample Mean for Smartphone A
The weights of Smartphone A are: 125, 124, 124, 126, 122, 126, 124, 123, 123, 126, 124.
First, sum all the weights:
\[
125 + 124 + 124 + 126 + 122 + 126 + 124 + 123 + 123 + 126 + 124 = 1367
\]
Next, divide by the number of samples (11):
\[
\bar{x}_A = \frac{1367}{11} = 124.272727
\]
Step 2: Calculate the Sample Mean for Smartphone B
The weights of Smartphone B are: 123, 123, 123, 125, 124, 121, 122, 123, 126, 123, 122, 125, 123.
First, sum all the weights:
\[
123 + 123 + 123 + 125 + 124 + 121 + 122 + 123 + 126 + 123 + 122 + 125 + 123 = 1578
\]
Next, divide by the number of samples (13):
\[
\bar{x}_B = \frac{1578}{13} = 121.384615
\]
Step 3: Find the Point Estimate of the Difference
Now, subtract the sample mean of Smartphone B from the sample mean of Smartphone A:
\[
\bar{x}_A - \bar{x}_B = 124.272727 - 121.384615 = 2.888112
\]
Therefore, the point estimate for the true difference between the population means is approximately 2.888112 when rounded to six decimal places.
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