Questions: Mary ∨ Homework ? Question 11 of 15 (1 point) Question Attempt: 1 of 10 Part 2 of 3 Espanat (b) Find the 90% confidence interval of the population mean. 36.76 < μ < 62.77 Part: 2 / 3 Part 3 of 3 (c) There is something unusual about the data. Describe it and state how it would affect the confidence interval. Choose the correct answer. There is an outlier in the data. This will affect the sample mean, and therefore the confidence interval, making it less likely to contain the population mean. There is an outlier in the data. This will not affect the sample mean, and therefore will not affect the confidence interval. There is no mode. This will make the confidence interval less likely to contain the population mean. The data is bimodal. This will make the confidence interval less likely to contain the population mean.

Mary ∨
Homework ?
Question 11 of 15 (1 point) Question Attempt: 1 of 10
Part 2 of 3
Espanat
(b) Find the 90% confidence interval of the population mean.
36.76 < μ < 62.77
Part: 2 / 3
Part 3 of 3
(c) There is something unusual about the data. Describe it and state how it would affect the confidence interval.

Choose the correct answer.
There is an outlier in the data. This will affect the sample mean, and therefore the confidence interval, making it less likely to contain the population mean.

There is an outlier in the data. This will not affect the sample mean, and therefore will not affect the confidence interval.
There is no mode. This will make the confidence interval less likely to contain the population mean.
The data is bimodal. This will make the confidence interval less likely to contain the population mean.

Transcript text: Mary $\vee$ Homework ? Question 11 of 15 (1 point) । Question Attempt: 1 of 10 Part 2 of 3 Espanat (b) Find the $90 \%$ confidence interval of the population mean. $36.76<\mu<62.77$ Part: $2 / 3$ Part 3 of 3 (c) There is something unusual about the data. Describe it and state how it would affect the confidence interval. Choose the correct answer. There is an outlier in the data. This will affect the sample mean, and therefore the confidence interval, making it less likely to contain the population mean. There is an outlier in the data. This will not affect the sample mean, and therefore will not affect the confidence interval. There is no mode. This will make the confidence interval less likely to contain the population mean. The data is bimodal. This will make the confidence interval less likely to contain the population mean. $\times$ 5 Checl Save For Later Submit Assignment 2024 McGraw Hill LLC. All Rights Reserved. Terms of Use

Solution

Solution Steps

Step 1: Calculate the Mean

The mean $ \mu $ of the data is calculated as follows:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} = \frac{99.53}{2} = 49.77 \]

Step 2: Calculate the Margin of Error

The Z-score for a 90% confidence level is $ Z = 1.6449 $. The margin of error $ E $ is calculated using the formula:

\[ E = Z \cdot \frac{\sigma}{\sqrt{n}} = 1.6449 \cdot \frac{10}{\sqrt{30}} \approx 3.0031 \]

Step 3: Calculate the Confidence Interval

The confidence interval for the mean is given by:

\[ \bar{x} \pm E = 49.77 \pm 3.0031 \]

Calculating the bounds:

\[ \text{Lower Bound} = 49.77 - 3.0031 \approx 46.77 \] \[ \text{Upper Bound} = 49.77 + 3.0031 \approx 52.77 \]

Thus, the confidence interval is:

\[ (46.77, 52.77) \]

Step 4: Describe the Unusual Data

There is an outlier in the data. This will affect the sample mean, and therefore the confidence interval, making it less likely to contain the population mean.