Question

which of the following gives the confidence interval? a. between 0.07 and 0.13 b. between 2.4 and 3.1 c. between 20.3 and 20.9

Answer 1

The confidence interval at the 90% confidence level is between 20.3 and 20.9 hours. Therefore, the correct answer is:

C) between 20.3 and 20.9

The margin of error in the context of a confidence interval for a mean is the value that is added to and subtracted from the sample mean to construct the interval. If the margin of error is 0.3 and the sample mean is 20.6, the confidence interval can be calculated by adding and subtracting the margin of error from the mean.

The formula for the confidence interval is:

`\[ \text{Confidence Interval} = \text{Sample Mean} \pm \text{Margin of Error} \]`

Given:

- Sample Mean
`(\( \bar{x} \))` = 20.6

- Margin of Error (E) = 0.3

Let's calculate the confidence interval:

`\[ \text{Lower Bound} = \bar{x} - E = 20.6 - 0.3 \]`

`\[ \text{Lower Bound} = 20.3 \]`

`\[ \text{Upper Bound} = \bar{x} + E = 20.6 + 0.3 \]`

`\[ \text{Upper Bound} = 20.9 \]`

The confidence interval at the 90% confidence level is between 20.3 and 20.9 hours. Therefore, the correct answer is:

C) between 20.3 and 20.9

Show all the calculation part step-wise in detailed manner.

A survey of 225 students showed the mean number of hours spent studying per week was 20.6 and the standard deviation was 2.7 Assuming a 90% confidence level, the margin of error is approximately 0.3 Which of the following gives the confidence interval? A) between 2.4 and 3.1 B) between 0.07 and 0.13 C) between 20.3 and 20.9