25 # Transcription for Educational Website## Serum Cholesterol Levels of L.A. County EmployeesThe serum cholesterol levels of 50 subjects randomly selected from the L.A. Heart Data, derived from a heart disease study on Los Angeles County employees, are displayed in the table below:| | | | | | | | | | ||---|---|---|---|---|---|---|---|---|---|| 148 | 307 | 297 | 242 | 370 | 137 | 206 | 248 | 270 | 298 || 298 | 317 | 172 | 214 | 257 | 170 | 166 | 249 | 212 | 256 || 262 | 279 | 270 | 229 | 261 | 237 | 250 | 219 | 270 | 302 || 282 | 226 | 215 | 263 | 218 | 245 | 182 | 199 | 250 | 259 || 229 | 225 | 303 | 183 | 245 | 280 | 186 | 270 | 276 | 248 |### Statistical Analysis and Interpretation1. **Creating a Confidence Interval**: - Since \( n > 30 \), use the methods from Chapter 8 to create a large-sample 95% confidence interval for the average serum cholesterol level of L.A. County employees. - **Answer format**: [lower bound] to [upper bound], rounded to three decimal places.2. **Using the t-distribution**: - Construct a 95% confidence interval, resulting in the interval \( 233.334 \) to \( 260.226 \). - Compare the two intervals. (HINT: The two intervals should be quite similar, highlighting why a z-distribution is used for approximation when \( n > 30 \).) \[ \bar{x} = \frac{x - \mu}{\sigma / \sqrt{n}} \]3. **Conclusion**: - Select which statement is true: - The two intervals are similar. - The two intervals are very different.### Educational FocusThis exercise illustrates the process of calculating confidence intervals based on sample data, emphasizing the comparative analysis when using different statistical methods, such as z-distribution and

Solution: n = 50 Sample size ∑x =12339x =∑x n=1233950=246.78 Sample mean s= ∑(x-x)2n-1s =47.3119 Sample standard deviation The 95% confidence interval for the average Cholestrol for L.A County employees is x±Zα/2×snAt α=0.05Zα/2=Z0.025=1.96 From Z table 246.78±1.96×47.311950246.78±1.96×47.31197.071068(246.78±1.96×6.690913)(246.78±13.114189)( 246.78-13.114189, 246.78+13.114189)(233.665811, 259.894189)(233.666, 259.894) The 95% confidence interval for the average Cholestrol for L.A County employees is 233.666 to 259.894 Using t distribution the 95% confidence interval for the average Cholestrol for L.A County employees is 233.334 to 260.226 The two interval are similar. Option A is Correct

Math

Statistics

The serum cholesterol levels of 50 subjects randomly selected from the LA. Heart Data, data from a heart disease study on Los Angeles County employees, are shown below. 148 307 297 242 370 137 208 248 270 228 298 317 172 214 257 170 166 249 212 256 262 279 270 229 261 237 250 219 270 302 282 226 215 263 218 245 182 199 250 259 309 225 203| 183 245 280 316 270 276 248 Since n> 30, use the methods of Chapter 8 to create a large-sample 95% confidence interval for the average serum cholesterol level for LA. County employees. (Round your answers to three decimal places.) to Using a t-distribution to construct a 95% confidence interval gives the interval 233.334 to 260.226. Compare the two intervals. (HINT: The two intervals should be quite similar. This is the reason we choose to approximate the sample distribution of with a z-distribution when n> 30.) O The two intervals are similar. are uepi difer