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 1m
- 3. Describing Data Numerically1h 48m
- 4. Probability2h 26m
- 5. Binomial Distribution & Discrete Random Variables2h 55m
- 6. Normal Distribution & Continuous Random Variables1h 48m
- 7. Sampling Distributions & Confidence Intervals: Mean2h 8m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 20m
- 9. Hypothesis Testing for One Sample2h 23m
- 10. Hypothesis Testing for Two Samples3h 25m
- 11. Correlation1h 6m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 30m
- 14. ANOVA1h 4m
7. Sampling Distributions & Confidence Intervals: Mean
Confidence Intervals for Population Mean
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Find the critical val. () for each confidence interval.
(B) Confidence Level =
A
2.41
B
2.68
C
1.68
D
1.30

1
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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