Question

A random sample of 81 individuals receiving unemployment benefits yields a mean time receiving those benefits of 42.3 weeks, with a standard deviation of 11.4 weeks.

(a) Check if the distribution of this sample mean follows normal and explain it.

(b) Find a 98% CI for the mean time receiving unemployment benefits. Write a sentence interpreting your CI.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 42.3

Population standard deviation =    = 11.4

Sample size = n =81

distribution of this sample mean follows normal because sample mean is given

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z_/2 = Z_0.01 = 2.326

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

= 2.326 * (11.4 /  81 )

= 2.9463
At 98% confidence interval estimate of the population mean
is,

- E < < + E

42.3 - 2.9463 <   < 42.3  + 2.9463

39.3537<   < 45.2463

(  39.3537, 45.2463 )

At 98% confidence interval estimate of the population mea is(  39.3537, 45.2463 )