Statistical Analysis and Probability: A Comprehensive Assignment on Hypothesis Testing, Probability Distributions, and Data Interpretation

Preview (3 of 7 Pages)

100%

Loading page ...

Statistical Analysis and Probability: A Comprehensive Assignmenton Hypothesis Testing, Probability Distributions, and DataInterpretation1.True or False.Justify for full credit.(a) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discretedata set.False-The value 128 is a measure of volume which is a continuousvariable and can have values other than counting numbers. A volume of 128.2for example is possible.(25 pts).(b)If the variance from a data set is zero, then all the observations in this data setmust be zero.False-Ifthe variance from a data set is zero, then all theobservations in this data set must be equal..(c)P(AANDAc)=0, whereAcis the complement ofA.True(AANDAc) is theintersectionof A and its complement and by definition it is null..(d)The mean and median for a normal distribution are always the same.True-The normal distribution isa bell-shaped distribution and symmetricalabout the mean, therefore the mean=median..(e)In a hypothesis testing, if the p-value is less than the significance level α, wedo nothave sufficient evidence to reject the null hypothesis.FalseIf thep-value is less than the significance level α, have sufficient evidence toreject the null hypothesis, since the test statistic lies in the rejectionregion.Refer to the following frequency distribution for Questions 2, 3, 4, and 5.Show allwork. Just the answer, without supporting work, will receive no credit.A random sample of 25 customers was chosen in UMUC MiniMart between 3:00 and4:00 PM on a Friday afternoon. The frequency distribution below shows thedistribution for checkout time (in minutes).Checkout Time (in minutes)FrequencyRelative Frequency1.0-1.96=6/25 *100=24

Loading page ...

2.0-2.98=8/25 *100=323.0-3.96244.0-5.95=5/25 *100=20Total251002. Complete the frequency table with frequency and relative frequency.3.What percentage of the checkout times was less than 3 minutes?=24+32=56%4.In what class interval must the median lie? Explain your answer.2.0-2.9,sincethe cumulative frequency corresponding to this interval is 56% and themedian which is the 50thpercentile is included in this interval.5.Assume that the largest observation in this dataset is 5.8. Suppose thisobservation wereincorrectly recorded as 8.5 instead of 5.8. Will the meanincrease, decrease, or remain the same? Will the median increase, decrease orremain the same? Why? (5 pts)The mean will increase, as thesum of theobservations is increased by 2.7 and the number of observations is the same.The medianremains the same, since only the highest observation was affected.Refer to the following information for Questions 6, 7, and 8.Show all work. Just theanswer, without supporting work, will receive no credit.A 6-faced die is rolled two times. Let A be the event that the outcome of the first rollis an even number, and B be the event that the outcome of second roll is greaterthan 4.6.How many outcomes are there in the sample space? (5 pts)A :3*6=18outcomesB:6*2=12outcomes7.What is the probability that the outcome of the second roll is greater than 4, giventhat the first roll is an even number? (10 pts)P(B|A)= P(AB)/P(A)P(A)= 18/6*6= 18/36 =1/2P(AB)=3*2/6*6 =1/6P(B|A)= P(AB)/P(A)=( 1/6)/1/2= 2/6=1/38.AreAandBindependent? Why or why not?Yes asP(AB)= P(A)*P(B)—1/6=½*1/3=1/6

Preview Mode

This document has 7 pages. Sign in to access the full document!

Report

Study Now!

Document Details

Related Documents

Statistics - Univariate Inferential Tests

Statistics - Sampling

Statistics - Probability

Statistics - Principles of Testing

Statistics - Numerical Measures

Statistics - Introduction to Statistics

Statistics - Graphic Displays

Statistics - Cummulative Reviews

Statistics - Common Mistakes and Tables

Statistics - Bivariate Relationships

Company

Explore

Study Tools