Question

1. Rocket Powered Roller Skates, let’s you skate at unlimited speeds. Find the 90% confidence interval of the true variance and the true standard deviation for the lifetime of ACME’s Rocket Powered Roller Skates if a random sample of 24 Rocket Powered Roller Skates has a standard deviation of 4.8 months. Assume that the lifetime of ACME’s Rocket Powered Roller Skates is normally distributed.

1. Find the critical values of χ2L and χ2R that corresponds to the confidence interval.

   χ 2L = , χ 2R =

2. Construct the confidence interval for the variance. Round the endpoints to two decimal places.

Answer:

c. Construct the confidence interval for the standard deviation. Round the endpoints to two decimal places.

Answer:
d. Write a sentence that interprets the context of the situation for the standard deviation.

Answer:

Answer 1

Given that, sample size (n) = 24 and

sample standard deviation (s) = 4.8 months

confidence level = 0.90

=> significance level = 1 - 0.90 = 0.10

Degrees of freedom = 24 - 1 = 23

Using Excel we find, the chi-square critical values as follows :

a)

b)

c) The confidence interval for the standard deviation is,

Therefore, required confidence interval is, (3.88, 6.36).

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d) Interpretation : We are 90% confident that the standard deviation for the lifetime of ACME’s Rocket Powered Roller Skates is between 3.88 and 6.36 months.