Question

The mean and standard deviation for the charge time of a random sample of 36 iPhones were found to be 23 and 2.5 hours respectively. Assuming that the charge time was normally distributed. A 99% confidence interval for the mean charge time is:

Select one:

a. 23 +/- 1.29

b. 23 +/- 1.40

c. 23 +/- 0.77

d. 23 +/- 1.14

e. 23 +/- 0.91

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 23

sample standard deviation = s = 2.5

sample size = n = 36

Degrees of freedom = df = n - 1 = 36 - 1 = 35

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2,df = t0.005,35 = 2.724

At 99% confidence level of is

  t/2,df * (s /n)

23 2.724 * (2.5 / 36)

23   1.14

option D. is correct