Revisit Survey data example We collected data on the longest relationship STAT 2

Question

Revisit Survey data example We collected data on the longest relationship STAT 226 students have been in. We are interested in the average length of the longest relationship and take a random sample of 36 observations. The sample yielded a mean of x= 17.37 months. We know the population standard deviation is = 19.495 months. Length of Relationship 250 200 150 100 -50 -15 0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 ength in months Fall 2017, Stat 226 (Sections L) Introduction to Business Statistics Module 5, Chapter 15 1528

Explanation / Answer

Solution1:

n=36

std dev=14.495

sample mean=17.37

z crit for 95%=1.96

95% confidence interval for the average length of the longest relationship that all current STAT 226 have been in

=sample mean-margin of error,sample mean+margin of error

margin of error=zcrit*stdev/sqrt(n)]

=1.96*19.495/sqrt(36)

=6.368367

therfore,

17.37-6.368367 and 17.37+6.368367

11.00163 and 23.73837

lower limit=11.00

upper limit=23.74

11<mu<23.74

Intrepretation:

We are 95% confident that the true average length of the longest relationsghip that all current STAT 226 have been in lies in between 11 and 23.74 months.

SOlutionc:

Increasing the confidenc elevel form 90 to 95% onfidence interval becomes wider.

the width of the confidence interval is affected by

n(sample size) and

z crit

As the confidence level incraeses,the multiplier Z crit increases,leading to a wider CI

Solutiond:

we can increase the precison of confidence interval by increasing sample size .

Increasing sample size also decreases error and we get a more precise estimate of population mean.

SOlutionf:

For 90% confidence interval z multiplier=1.645

For 95%confidence interval z multiplier=1.96

increasing confidence level form 90% to 95% z crit value increases.

Solutiong:

If we use the sample standard deviation instead of population standard deviation.We have to use t critical for n-1 degrres of freedom instead of Z critical

SOlutionh:

YES.we can also get the cconfidence interval for population proportion,population standard deviation.

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