Question

2. P337. 23. A large box contains 10,000 ball bearings. A random sample of 120 is chosen. The sample mean diameter is 10 mm, and the standard deviation is 0.24 mm. True or false: (a) A 95% con dence interval for the mean diameter of the 120 bearings in the sample is 1 ???? (1:96)(0:24)= p 120. (b) A 95% con dence interval for the mean diameter of the 10,000 bearings in the sample is 1 ???? (1:96)(0:24)= p 120. (c) A 95% con dence interval for the mean diameter of the 10,000 bearings in the sample is 1 ???? (1:96)(0:24)= p 10; 000.

Answer 1

B is True

A, C. D are false

Explanation:

Given :

Sample size, n = 120

Mean diameter, m = 10

Standard deviation, s = 0.24

Confidence level, Zcritical ; Z0.05/2 = Z0.025 = 1.96

The confidence interval represents how the true mean value compares to a set of values around the mean computed from a set of sample drawn from the population.

The population here is N = 10000

To obtain

Confidence interval (C. I) :

Mean ± margin of error

Margin of Error = Zcritical * s/sqrt(n)

Margin of Error = 1.96 * 0.24/sqrt(120)

Confidence interval for the 10,000 ball bearing :

10 ± 1.96 * (0.24) / sqrt(120)

Hence. The confidence interval defined as :

10 ± 1.96 * (0.24) / sqrt(120) is the 95% confidence interval for the mean diameter of the 10,000 bearings in the box.