A Single Population Mean using the Student t Distribution · Exercise 29

Suppose that 14 children, who were learning to ride two-wheel bikes, were surveyed to determine how long they had to use training wheels. It was revealed that they used them an average of six months with a sample standard deviation of three months. Assume that the underlying population distribution is normal.

(a) (a) $\bar{x}$ = __________
(b) $s_x$ = __________
(c) n = __________
(d) n – 1 = __________
(b) Define the random variable $X$ in words.
(c) Define the random variable$\bar{X}$ in words.
(d) Which distribution should you use for this problem? Explain your choice.
(e) Construct a 99% confidence interval for the population mean length of time using training wheels.
(a) State the confidence interval.
(b) Sketch the graph.
(c) Calculate the error bound.
(f) Why would the error bound change if the confidence level were lowered to 90%?

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Statistics 2e · §8.2 A Single Population Mean using the Student t Distribution · Exercise 29