Question

A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape.

389	356	359	363	376	424	326	395	402
373	374	371	364	366	365	325	339	394
392	369	375	359	356	403	335	398

A normal probability plot of the n = 26 observations on escape time given above shows a substantial linear pattern; the sample mean and sample standard deviation are 371.08 and 24.35, respectively. (Round your answers to two decimal places.)

(a)

Calculate an upper confidence bound for population mean escape time using a confidence level of 95%.

(b)

Calculate an upper prediction bound for the escape time of a single additional worker using a prediction level of 95%.

How does this bound compare with the confidence bound of part (a)?

The upper prediction bound is lower than the upper confidence bound. The upper prediction bound is higher than the upper confidence bound.     The upper prediction bound is equal to the the upper confidence bound.

(c)

Suppose that two additional workers will be chosen to participate in the simulated escape exercise. Denote their escape times by

X₂₇

and

X₂₈,

and let

X_new

denote the average of these two values. Modify the formula for a PI for a single x value to obtain a PI for

X_new,

and calculate a 95% two-sided interval based on the given escape data.

Answer 1

a)

Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   25          
't value='   tα/2=   2.0595   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   24.3500   / √   26   =   4.775428
margin of error , E=t*SE =   2.0595   *   4.77543   =   9.835178
                  
confidence interval is                   

Interval Upper Limit = x̅ + E =    371.08   -   9.835178   =   380.915178

b)

margin of error for prediction interval,E=   t*s*√(1+1/n)=   51.1051
prediction interval is       

Interval Upper Limit=   x̅ + E =    422.1851

The upper prediction bound is higher than the upper confidence bound

THANKS

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