Exam_1

.xlsx

School

University of Miami *

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Course

660

Subject

Statistics

Date

Apr 3, 2024

Type

xlsx

Pages

241

Uploaded by MasterPigeonPerson384

half-time of a sporting event. The half-time is 25 minutes long. Beginning ea had decided to practice the performance on 50 independent occasions which and she has made a list of how long it has taken her to play the sonata from of these 50 trial performances. From the collected data, the observed samp 22 minutes, and the observed sample standard deviation from the sample da (a) (2 points) Construct a 90% confidence interval for the true mean perfor Remember to show work/formulas/etc. In particular, if you need t not contained in the problem statement, such as c, be sure to show 22 +/- Lower bound of CI 21.534765 Upper bound of CI 22.465235 have decided to practice the performance (and record the corres n 106.158 107 1. (3 pts, total) A pianist is performing Rachmaninoff's 2 nd Piano Sonata tom (b) (1 point) Experimental design: In hindsight, taking the above sample as a a 99% confidence interval for the mean performance time that h

arlier this year, the pianist h she has already done, start to finish in each ple mean performance time of the 50 performances is ata is 2 minutes. rmance time. to find values w work for how you obtain values. 0.465234861470669 B 90 C 1.644854 N 50 Xbar 22 s 2 sponding data) so that she would have been able to construct B 99 C 2.575829 S 2 L 0.5 morrow, during the a given pilot sample, how many times should the pianist has a tolerance level of L = 30 seconds, i.e. if she wanted her 99% CI to look like x-bar plus/minus 30 sec

conds.

Further suppose that a 95% confidence interval for the mean Iowan household in Justificatio The are th 2. (2 points, total) Suppose that annual household income has been recorded for a random sample o a) (1 pt) Would a 99% confidence interval be wider or narrower than the one above? i) The 99% confidence interval would be wider. ii) The 99% confidence interval would be narrower. b) (1 pt) The 95% confidence interval can be correctly interpreted as which of the follo i) If the true mean Iowan household income is outside of the inte ii) There is a 95% chance that the true mean Iowan household inco iii) There are 5% of Iowan households that have household income

ncome has been constructed (based on the above sample data) and is (44358, 65892). on: hat could contain mean is larger 2.326>1.645 99%>95% of 100 households in the state of Iowa. Highlight your selection, and provide a brief justification of your answer. owing? (Highlight your selection, no justification needed): erval (44358, 65892), then a particular event has occurred which had only a 5% chance of occurring. ome is between 44358 and 65892. es outside of the interval (44358, 65892).

Assume the travel time of a given trip is a random variable that is normally distributed with a m Further assume that from one day to the next, trip times are independent of each other. 0.022750132 X 6 u 5 STD 0.5 2 (Your answer should be an exact answer with an Excel formula coded into your cell. 0.827639388 P 0.02275 P(5=<X=<15) 0.161877613 0.989517001 0.827639388 3. (5 pts, total) Suppose that the Iowa Express is a super-speedy train that makes daily trips (one trip per a) (2 pts) What is the probability that the travel time on a given day is over 6 hours? (You b) (1 pt) What is the z-score associated to a trip travel time of 6 hours? c) (2 pts) What is the probability that over the course of a 365 day year, between 5 and 1

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