Suppose that we have the the following data on the amount of pressure it takes t

Question

Suppose that we have the the following data on the amount of pressure it takes to crack a certain type of tempered glass (in the 1000s of psi):

7.2, 9.4, 8.3, 8.7, 7.5, 8.1

7.2 9.4 8.3 8.7 7.5 8.1 If we assume that this data in normally distributed, find point estimates for each of the following. a) The population mean. b) The population variance c) The value that separates the largest 9% of all values in the distribution of pressures from the smallest 91%. d) The standard error of your estimator in part a.

Explanation / Answer

solution A:

estimate of population mean=sample mean=x bar

=sum/total

=7.2+9.4+ 8.3+ 8.7+7.5+8.1/5

=49.2/6

sample mean=8.2

Solutionb:

estimator of population variance=sample variance =0.64

We will compute this formula in 4 steps.

Step 1: Find the mean. (X¯¯¯)

here: X¯¯¯=8.2.

Step 2: Create the following table.

Step 3: Find the sum of numbers in the last column to get.

(xiX¯¯¯)2=3.2

Step 4: Calculate variance using the above formula.

var=(xiX¯¯¯)2/n1=3.2/61=0.64

Solutionc:

critical value is 91% and confidence level is 1.70

z=1.7

x to b efound

x bar=8.2

s=0.8

z=x-mean/stddev

1.7=x-8.2/0.8

9.56

Annswer 9.56

Solutiond:

standard error=SE=

=sqrt(0.64)/sqrt(6)

=0.327

data data-mean (data - mean)2 7.2 -1 1 9.4 1.2 1.44 8.3 0.1 0.01 8.7 0.5 0.25 7.5 -0.7 0.49 8.1 -0.1 0.01

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