Understanding Confidence Intervals: Examined & Explained

Final Exam - Results Attempt 1 of 1 Written Apr 2, 2024 1:31 PM - Apr 2, 2024 3:39 PM Released Apr 3, 2024 12:00 PM Attempt Score 94.67 / 100 - 94.67 % Overall Grade (Highest Attempt) 94.67 / 100 - 94.67 % What is a Confidence Interval Question 1 3 / 3 points With 95% confidence, the program director estimated that the proportion of MGMT650 students that are very satisfied is 90% ± 5%. It's in the top 10% of all classes. What is a Confidence Interval The proportion of very satisfied students cannot be off by more than 5%. With 95% probability, the true proportion of very satisfied students falls between 85% and 95%. Loosely, we say with 95% confidence that the true proportion is somewhere between 85% and 95%. Actually, 95% of all possible confidence intervals contain the true proportion. There is a 5% probability that the true proportion of very satisfied students falls between 85% and 95%.

Question 2 3 / 3 points Answer: 0.54 Hide ques²on 2 feedback Margin of Error - Mean Question 3 4 / 4 points What is the margin of error for the population mean at 90% confidence level for the information in DATA (<--- Click the link to access the data for this problem.) With 80% confidence, for sample proportion 0.42 and sample size 28, what is the upper confidence limit with 2 decimal places? With 80% confidence, for sample proportion p and sample size n, the upper confidence limit is p + NORM.S.INV(1 - (1 - 0.80)/2) x SQRT( p(1-p)/n ) Margin Mean 0.72 0.76 None of the answers match my calculation. 0.75 0.74 0.73 0.71

Hide ques²on 3 feedback Question 4 3 / 3 points Answer: 327.10 Hide ques²on 4 feedback Confidence Interval - Test Mean Question 5 4 / 4 points Bobo's Bad Burgers fast food claims you will be in and out in 5 minutes. To test this claim, time in minutes from entering Bobo's to receiving the order was secretly recorded. The results are documented in DATA. At a 95% confidence level, does the confidence interval support Bobo's claim? For sample mean m, sample standard deviation s, and sample size n, the margin of error is =T.INV.2T(1 - 0.90, n - 1) x s/SQRT(n) With 90% confidence, for sample mean 323.50, sample standard deviation 12.60, and sample size 35, what is the upper confidence limit with 2 decimal places? With 90% confidence, for sample mean m, sample standard deviation s, and sample size 35, the upper confidence limit is m + ( T.INV.2T(1 - 0.90, 35 - 1) x s/SQRT(35) ) Confidence Interval - 1 The confidence limits (4.77,6.58) support the claim of 5 minutes. 5 falls inbetween the confidence limits. Bobo's performance meets the expectation.

Question 6 3 / 3 points Match up the following: __ 4__ __ 1__ __ 3__ __ 2__ 1 . 2 . 3 . 4 . Question 7 4 / 4 points Match up the following: __ 2__ __ 1__ 1 . 2 . 3 . 4 . None of the answers match my calculation. The confidence limits (2.77, 4.54) reject the claim of 5 minutes. 5 is greater than the upper confidence limit. Bobo's performance is exemplary. The confidence limits (6.79,8.56) reject the claim of 5 minutes. 5 is less than the lower confidence limit. Audit of Bobo's procedures and employees is recommended. The confidence limits (1.62,3.21) reject the claim of 5 minutes. 5 is greater than the upper confidence limit. Performance at Bobo's is incredible. The risk we are willing to take of a type 1 error, or the type 1 error rate Rejection of H0 when H0 is true Rejection of H0 when H0 is false, or not rejecting H0 when H0 is true Failure to reject H0 when H0 is false Type 1 error Type 2 error Not an error The power of a test = P(rejecting H 0 |H 0 false) The probability of a type 2 error 1 - pvalue < H 0 : μ ≤ 0

__ 4__ __ 6__ __ 5__ __ 3__ 5 . 6 . Question 8 3 / 3 points Match the rules for rejecting H0 at the right to the following tests __ 3__ __ 2__ __ 4__ __ 1__ 1 . 2 . 3 . 4 . Question 9 3 / 3 points Match problems to procedures. Test of this hypothesis requires 1-tailed test with upper reject region Test of this hypothesis requires 2-tailed test with lower reject region bounded by negative critical value and upper reject region bounded by positive critical value Test of this hypothesis requires 1-tailed test with lower reject region bounded by negative critical value Reject H 0 H 0 : μ ≥ 0 H 0 : μ = 0 Two-tail test with lower and upper reject regions One-tail test with lower reject region For any test hypothesis, ANOVA, or Chi Squared, this rule for rejecting H0 always applies. One-tail test with upper reject region test statistic > positive critical value test statistic < negative critical value test statistic outside interval (negative critical value, positive critical value) pvalue <