Question

1. A high school principal is interested in the amount of time her students spend per week working at an after school job. 37 students are randomly selected and their working hours are recorded. The sample had a mean of 12.3 hours and a standard deviation of 11.2 hours. We would like to construct an 80% confidence interval for the population mean hours worked weekly by high school students.
   1. What critical value will you use for an 80% confidence interval? Give the value and specify whether it comes from the standard normal distribution or the t distribution ( or ).

_______________

1. Calculate the margin of error, E. (You must show the setup to receive credit. You may round to three decimal places, if needed.)

E = _______________

2. Construct the 80% confidence interval for the population mean hours worked weekly by high school students. (Round limits to one decimal place.)

_______________<  < _______________

  

Answer 1

Solution :

degrees of freedom = n - 1 = 37 - 1 = 36

a) t/2,df = t0.10,36 = 1.306

b) Margin of error = E = t/2,df * (s /n)

= 1.306 * (11.2 / 37)

Margin of error = E = 2.405

c) The 80% confidence interval estimate of the population mean is,

- E < < + E

12.3 - 2.405 < < 12.3 + 2.405

9.9 < < 14.7