Question

A random sample of 36 size AA batteries for toys yield a mean life of 6 hours with a sample standard deviation, 0.56 hours.

(a)

[3 pts] What process of finding confidence interval you would choose and why? Find appropriate critical value zα/2 or tα/2 (positive value only):

(b)

[4 pts] Find the margin of error:

(c)

[4 pts] Find the confidence interval:

(d)

[4 pts] Interpret the confidence Interval:

Answer 1

(a) Since , the population standard deviation is not known

Therefore, use t-distribution.

Now , df=degrees of freedom=n-1=36-1=35

Assume that the significance level=

Therefore , ; The Excel function is , =TINV(0.05,35)

(b) The margin of error is ,

(c) The 95% confidence interval is ,

(d) Interpretation : There are 95% confident that the true mean of population is lies in the interval (5.8105,6.1895)