Question

1. Over a sample of 47 voyages. Mr. Sulu found the Starship Enterprise traveled a mean of 658 light-years-per-dilithium-crystal (lypdc) with a standard deviation of 76 lypdc.

(a) Find a point estimate for the mean lypdc on all starship voyages.



(b) Find the 95% margin of error for the estimate in (a).






(c) Make a 95% confidence interval for the mean lypdc on all starship voyages. Interpret the interval.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 658

Population standard deviation =    =76

Sample size n =47

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96 * (76 / 47 )

= 21.7
At 95% confidence interval
is,

- E < < + E

658 - 21.7 <   < 658+ 21.7

(636.3, 679.7)