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Try to fix wording
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ismayc committed Sep 29, 2024
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Expand Up @@ -1470,7 +1470,7 @@ The problem at hand could be that the chocolate-covered almonds' weight for almo

We now provide the mathematical details for this problem. We assume that for the chocolate-covered almonds' weight the population mean and standard deviation are given by $\mu_1$ and $\sigma_1$ and for the chocolate-covered coffee beans' weight the population mean and standard deviation are given by $\mu_2$ and $\sigma_2$.

Our sampling exercise has now two components. First, we take a random sample of size $n_1$ from the almonds' bowl and find the sample mean. As we did before, we can let $\overline X_1$ represent the possible values that the sample mean can take for each possible sample. Second, we let $n_2$ represent the sample size used for samples from the coffee beans' bowl and the random variable $\overline X_2$ represent the possible values that the sample mean can take for each possible sample. To compare these two sample means, we look at the difference, $\overline X_1 - \overline X_2$. The distribution of $\overline X_1 - \overline X_2$ is the sampling distribution of the difference in sample means.
Our sampling exercise has two components. First, we take a random sample of size $n_1$ from the almonds' bowl and find the sample mean. We let $\overline X_1$ represent the possible sample mean values for each possible almond sample. Then, we let $n_2$ and $\overline X_2$ represent similar quantities for the coffee beans' bowl. To compare these two sample means, we look at the difference, $\overline X_1 - \overline X_2$. The distribution of $\overline X_1 - \overline X_2$ is the sampling distribution of the difference in sample means.

The expected value and standard error of $\overline X_1 - \overline X_2$ is given by $\mu_1 - \mu_2$ and

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