Question

On Arvala-7, Jawas are notorious for stealing parts from unattended vehicles. The number of part thefts over a one-month period in 40 randomly selected regional zones have a mean of 5.5 thefts and a standard deviation of 5.8 thefts.

1) Find the standard error for the number of parts thefts on Arvala-7.

2) Construct a 95% confidence interval for the true mean number of such thefts.

3) Interpret the confidence interval by stating your answer in a carefully worded sentence.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 5.5

sample standard deviation = s = 5.8

sample size = n = 40

Degrees of freedom = df = n - 1 = 40 - 1 = 39

1) SE = (s /n) = ( 5.8 / 40) = 0.917

2) At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t0.025,39 = 2.023

Margin of error = E = t/2,df * SE

= 2.023 * 0.917

Margin of error = E = 1.86

The 95% confidence interval estimate of the population mean is,

  ± E

= 5.5  ± 1.86

= ( 3.64, 7.36 )

3) We are 95% confident that the true mean of part thefts over a one-month period between 3.64 and 7.36.