You want to purchase one of the new Altima. You randomly select 400 dealerships across the United States and find a mean of \$25,000. Assume a population standard deviation of \$2500. Construct and interpret a 94% confidence interval for the true mean price for the new Nissan Altima.
Table of contents
- 1. Introduction to Statistics53m
- 2. Describing Data with Tables and Graphs2h 2m
- 3. Describing Data Numerically2h 8m
- 4. Probability2h 26m
- 5. Binomial Distribution & Discrete Random Variables3h 28m
- 6. Normal Distribution & Continuous Random Variables2h 21m
- 7. Sampling Distributions & Confidence Intervals: Mean3h 37m
- Sampling Distribution of the Sample Mean and Central Limit Theorem19m
- Distribution of Sample Mean - ExcelBonus23m
- Introduction to Confidence Intervals22m
- Confidence Intervals for Population Mean1h 26m
- Determining the Minimum Sample Size Required12m
- Finding Probabilities and T Critical Values - ExcelBonus28m
- Confidence Intervals for Population Means - ExcelBonus25m
- 8. Sampling Distributions & Confidence Intervals: Proportion2h 20m
- 9. Hypothesis Testing for One Sample5h 15m
- Steps in Hypothesis Testing1h 13m
- Performing Hypothesis Tests: Means1h 1m
- Hypothesis Testing: Means - ExcelBonus42m
- Performing Hypothesis Tests: Proportions39m
- Hypothesis Testing: Proportions - ExcelBonus27m
- Performing Hypothesis Tests: Variance12m
- Critical Values and Rejection Regions29m
- Link Between Confidence Intervals and Hypothesis Testing12m
- Type I & Type II Errors16m
- 10. Hypothesis Testing for Two Samples5h 35m
- Two Proportions1h 12m
- Two Proportions Hypothesis Test - ExcelBonus28m
- Two Means - Unknown, Unequal Variance1h 2m
- Two Means - Unknown Variances Hypothesis Test - ExcelBonus12m
- Two Means - Unknown, Equal Variance15m
- Two Means - Unknown, Equal Variances Hypothesis Test - ExcelBonus9m
- Two Means - Known Variance12m
- Two Means - Sigma Known Hypothesis Test - ExcelBonus21m
- Two Means - Matched Pairs (Dependent Samples)42m
- Matched Pairs Hypothesis Test - ExcelBonus12m
- Two Variances and F Distribution29m
- Two Variances - Graphing CalculatorBonus15m
- 11. Correlation1h 24m
- 12. Regression3h 42m
- Linear Regression & Least Squares Method26m
- Residuals12m
- Coefficient of Determination12m
- Regression Line Equation and Coefficient of Determination - ExcelBonus8m
- Finding Residuals and Creating Residual Plots - ExcelBonus11m
- Inferences for Slope32m
- Enabling Data Analysis ToolpakBonus1m
- Regression Readout of the Data Analysis Toolpak - ExcelBonus21m
- Prediction Intervals13m
- Prediction Intervals - ExcelBonus19m
- Multiple Regression - ExcelBonus29m
- Quadratic Regression23m
- Quadratic Regression - ExcelBonus10m
- 13. Chi-Square Tests & Goodness of Fit2h 31m
- 14. ANOVA2h 32m
7. Sampling Distributions & Confidence Intervals: Mean
Confidence Intervals for Population Mean
Multiple Choice
You ask 16 people in your Statistics class what their grade is. The data appears to be distributed normally. You find a sample mean and sample standard deviation of 60 and 24, respectively. Construct and interpret a 95% confidence interval for the population mean class grade.
A
(10.14, 37.86); We are 95% confident that the interval for the population mean class grade falls in between 10.14 and 37.86.
B
(47.214, 72.786); We are 95% confident that the interval for the population mean class grade falls in between 47.214 and 72.786
C
(-10.65, 58.65); We are 95% confident that the interval for the population mean class grade falls in between -10.65 and 58.65.
D
(25.35, 94.65); We are 95% confident that the interval for the population mean class grade falls in between 25.35 and 94.65.
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Verified step by step guidance1
Identify the sample mean (\( \bar{x} \)) and sample standard deviation (\( s \)) from the problem. Here, \( \bar{x} = 60 \) and \( s = 24 \).
Determine the sample size (\( n \)), which is 16 in this case.
Since the sample size is less than 30 and the population standard deviation is unknown, use the t-distribution to find the critical value. For a 95% confidence interval and \( n - 1 = 15 \) degrees of freedom, find the t-value from the t-distribution table.
Calculate the standard error of the mean (SEM) using the formula: \( \text{SEM} = \frac{s}{\sqrt{n}} \). Substitute the values to find the SEM.
Construct the confidence interval using the formula: \( \bar{x} \pm (t \times \text{SEM}) \). Substitute the sample mean, t-value, and SEM to find the lower and upper bounds of the confidence interval.
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