Question

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 elevenmonths with a sample standard deviation of three months. Assume that the underlying population distribution is normal.

1. Which distribution should you use for this problem? (Enter your answer in the form z or t_df where df is the degrees of freedom.)

2. Construct a 99% confidence interval for the population mean length of time using training wheels.

(i) State the confidence interval. (Round your answers to two decimal places.)

(iii) Calculate the error bound. (Round your answer to two decimal places.)

3. (f) Why would the error bound change if the confidence level were lowered to 90%?

When the confidence level decreases, the error bound for the confidence interval increases.When the confidence level changes, the interval does not change.     When the confidence level decreases, the error bound for the confidence interval decreases as well.When the confidence level increases, the error bound for the confidence interval decreases.When the confidence level increases, the error bound for the confidence interval increases as well.

Answer 1

1)

t distribution

df = 14 - 1 = 13

2)

1)

sample mean, xbar = 11
sample standard deviation, s = 3
sample size, n = 14
degrees of freedom, df = n - 1 = 13

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, tc = t(α/2, df) = 3.012

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (11 - 3.012 * 3/sqrt(14) , 11 + 3.012 * 3/sqrt(14))
CI = (8.59 , 13.41)

2)

ME = tc * s/sqrt(n)
ME = 3.012 * 3/sqrt(14)
ME = 2.41

3)

When the confidence level decreases, the error bound for the confidence interval decreases as well