Question

The principal randomly selected six students to take an aptitude test.

Their scores were 79 88 83 80 72 78 Assume that the population is normally distributed.

a) Check assumptions and determine an appropriate interval procedure.

b) Find a 90% confidence interval for the mean score for all students. (Do not use any functions in TI=>STAT=>TESTS to show your work.)

c) Interpret the confidence interval.

Answer 1

Answer:

79, 88, 83, 80, 72, 78

n= 6, c= 90%

now calculate the sample mean and sample standard deviation

we get,

= 80, s = 5.3291650377897

a) assumption to carry appropriate t interval procedure are as follows,

i) sample is drawn from normally distributed population.

ii) sample is a simple random sample

iii) sample is less than 10% of population.

thus all above assumptions are met.

b)

formula for confidence interval is

Where tc is the t critical value for c =  90% with df = n -1 = 6 -1 = 5

tc= 2.015

75.616 < < 84.384

( 75.616 , 84.384 )

we get confidence interval as ( 75.616 , 84.384 )

c)

Therefore we are 90% confident that average score for aptitude test

lies between  75.616 to 84.384