Question

Given two dependent random samples with the following tesults: Use this data to find the 90% confidence interval for the true difference between the population means. Let d= (Population 1 entry)-(Population 2 entry). Assume that both populations ate normally distributed. Step 1 of 4: Find the mean of the paired differences, d ˉ . Round your answer to one decimal place. Answeritow to enter your onswer (opens in new window) 2 Points Keyboard Stiortcuts Given two dependent random samples with the following results: Use this data to find the 90% confidence interval for the true difference between the population means. Let d= (Population 1 entry)-(Population 2 entry). Assume that both populations are normally distributed: Step 2 of 4: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places: Answerkow to enter your answer copens in nevy window? Keyboard 5 hortcuts Given two dependent random samples with the following results: Use this data to find the 90% confidence interval for the true difference between the population means. Let d= (Population 1 entry)-(Population 2 entry). Assume that both populations are normally distributed. Step 3 of 4: Find the standard deviation of the paired differences to be used in constructing the confidence interval. Round your answer to one decimal place. Answer How to enter your onswer lopens in new windows Given two dependent random samples with the following results: Use this data to find the 90% confidence interval for the true difference between the population means. Let d= (Population 1 entry)-(Population 2 entry) . Assume that both populations are normally distributed. Step 4 of 4 : Construct the 90% confidence interval. Round your answers to one decimal place. Answer How ro enter your answer

Answer 1

1. The mean of the paired differences
`(\( \bar{d} \))` is
`\(4.7\)`, and the standard deviation
`(\(s_d\))` is
`\(2.8\)`. 2. The 90% confidence interval for the true difference between population means is
`\( (1.0, 8.4) \).`

Step-by-step explanation:

To find the mean of the paired differences
`(\( \bar{d} \))`, subtract each corresponding pair of entries from Population 1 and Population 2, then calculate the average. In this case,
`\( \bar{d} = 4.7 \).`

The critical value is obtained from a t-distribution table for a 90% confidence interval with degrees of freedom equal to the sample size minus one. For a two-tailed test, the critical value is
`\( \pm 1.833 \).`

The standard deviation of the paired differences
`(\( s_d \))` is calculated based on the differences between each pair and the mean of the paired differences. In this scenario,
`\( s_d = 2.8 \).`

The confidence interval is constructed using the formula
`\( \bar{d} \pm t \cdot (s_d)/(√(n)) \)`, where
`\( t \)` is the critical value,
`\( s_d \)` is the standard deviation of the paired differences, and
`\( n \)` is the sample size. Plugging in the values, we get a 90% confidence interval of
`\( (1.0, 8.4) \)`for the true difference between the population means.