Answer :
the point estimate for the true difference between the given population means is 0.320000.
To find the point estimate for the true difference between the given population means, the following data has been given:
Weights (in Grams) of Candy Bar A: 122, 122, 122, 121. 121, 120, 121, 122, 121, 123, 121
Weights (in Grams) of Candy Bar B: 118, 124, 122, 124. 122, 120, 122, 124. 118, 122, 119, 124. 121
The sample mean of Candy Bar A is equal to
(122 + 122 + 122 + 121 + 121 + 120 + 121 + 122 + 121 + 123 + 121)/11 = 121.63
The sample mean of Candy Bar B is equal to
(118 + 124 + 122 + 124 + 122 + 120 + 122 + 124 + 118 + 122 + 119 + 124 + 121)/13 = 121.31
So, the point estimate for the true difference between the given population means is:
121.63 - 121.31 = 0.32
Round the above answer to six decimal places. Therefore, the point estimate for the true difference between the given population means is 0.320000.
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Rounded to six decimal places, the point estimate for the true difference between the population means is 0.181818.
The point estimate for the true difference between the population means of the weights of Candy Bar A and Candy Bar B can be calculated by finding the sample means of each group and then subtracting one from the other.
First, calculate the sample mean for Candy Bar A:
[tex]\[ \bar{x}_A = \frac{\sum x_A}{n_A} = \frac{122 + 122 + 122 + 121 + 121 + 120 + 121 + 122 + 121 + 123 + 121}{11} = \frac{1344}{11} = 122.1818 \][/tex]
Next, calculate the sample mean for Candy Bar B:
[tex]\[ \bar{x}_B = \frac{\sum x_B}{n_B} = \frac{118 + 124 + 122 + 124 + 122 + 120 + 122 + 124 + 118 + 122 + 119 + 124 + 121}{13} = \frac{1586}{13} = 122.0000 \][/tex]
Now, find the difference between the two sample means to get the point estimate:
[tex]\[ \text{Point Estimate} = \bar{x}_A - \bar{x}_B = 122.1818 - 122.0000 = 0.1818 \][/tex]
