You want to take a trip to Paris. You randomly select 225 flights to Europe and find a mean and sample standard deviation of \$1500 and \$900, respectively. Construct and interpret a 95% confidence interval for the true mean price for a trip to Paris.
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
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- Linear Regression & Least Squares Method26m
- Residuals12m
- Coefficient of Determination12m
- Regression Line Equation and Coefficient of Determination - ExcelBonus8m
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- Enabling Data Analysis ToolpakBonus1m
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- 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
Find the critical val. () for each confidence interval.
(B) Confidence Level =
A
2.41
B
2.68
C
1.68
D
1.30
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Verified step by step guidance1
Step 1: Understand the problem. We are tasked with finding the critical value (t_{α/2}) for a 90% confidence level with a sample size of n = 48. The critical value is used in constructing confidence intervals and depends on the confidence level and degrees of freedom.
Step 2: Calculate the degrees of freedom (df). For a t-distribution, the degrees of freedom are given by df = n - 1, where n is the sample size. In this case, df = 48 - 1.
Step 3: Determine the value of α. The confidence level is 90%, so α = 1 - 0.90 = 0.10. Since we are looking for t_{α/2}, divide α by 2 to get α/2 = 0.10 / 2.
Step 4: Use a t-distribution table or statistical software to find the critical value t_{α/2}. Look up the value corresponding to α/2 and the calculated degrees of freedom (df).
Step 5: Verify the critical value. Ensure that the value obtained matches the confidence level and degrees of freedom provided in the problem.
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