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Math 1P98 - Practical Statistics Assignment

Added on - 15 Apr 2020

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Question 1(a)The summary statistics for the variable duration (Sec) is presented below:Confidenceinterval=Mean±Confidencelevel(93.0%)Upperlimit=229.61+4.08=233.69Lowerlimit=229.614.08=225.53Hence, 93% confidence interval is[225.53233.69]The t value with the help of T.INV.2T has computed through excel and is highlighted below:1
Thet2value comes out to be 2.120.(b)The summary statistics is shown below:97%Confidenceinterval=Mean±Confidencelevel(97.0%)Upperlimit=3.28+0.82=2.46Lowerlimit=3.280.82=4.11Hence, 93% confidence interval is[2.464.11]Question 2a)The requisite hypotheses are as stated below.Null Hypothesis (H0): μ ≥ 7 i.e. average rating of men would be atleast 7 out of 10Alternative Hypothesis (H1): μ < 7 i.e. average rating of men would be lesser than 7 out of 102
b)The relevant test statistic for this test would be z as the population variance is known and thesample size is greater than 30.Relevant Formula for Z test statistic = (X-μ)/SEIn the given case, X = 6.14, μ = 7, SE = σ/√n = 1.73/√187 = 0.1265Hence, calculated Z statistic = (6.14 -7)/(0.1265) = -6.80c)In accordance with the table A-2, the necessary p value for the above value of test statisticcomes out as 0.0001.d)It is apparent that the computed p value (0.0001) is lower than the given significance level of1% or 0.01. As a result, there exists enough statistical evidence to cause null hypothesisrejection and acceptance of alternative hypothesis. Thus, it would be appropriate to concludethat average attractiveness rating of men is lower than 7.e)It would be inappropriate to consider that 99% of the males would get an attractiveness ratinglesser than 7. This is one of the shortcomings of the inferential statistical techniques as theytend to ignore the inherent difference in the variable under consideration and tend to providean average view which may not apply to the concerned individual with a high consistency.This is especially the case for men attractiveness rating where there would be considerabledifference amongst individuals.Question 3a)The requisite hypotheses are indicated below.Null Hypothesis (H0) μ = 60 seconds3
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