Question

You measured the moisture content of 16 tubes of a cosmetic product that your company had recently developed. The 16 tubes were selected at random from a large shipment. The results are given in the table below. What is the range of moisture content that 95% of the tubes are expected to have? What is the estimate of the true mean moisture content for your shipment (P 95%)? The mean moisture content for this product should be 10%. Based on your measurements, does your product meet the specification with 95% confidence? Your company desire to reduce the confidence interval for the average of the moisture content to 0.1% (P-95%). Assuming the standard deviation remains unchanged, what is the minimum number of tubes you must measure to achieve a confidence interval of 0.1% (P-95%). (10 marks) 1. Moisture Content(%) 9.4 10.2 10.3 9.0 10.5 10.3 10.5 9.5 9.5 9.8 9.9 10.1 10.1 9.9 9.7 9.5

Answer 1

From the data,

Sample Mean moisture content = 9.8875%

Sample Standard deviation of moisture content, s = 0.4318565%

Degree of freedom = 16 - 1 = 15

Critical value of t for df = 15 and 95% confidence is 2.13

Range of moisture content that 95% of tube expected to have is,

(9.8875 - 0.4318565 * 2.13, 9.8875 + 0.4318565 * 2.13)

= (8.9676%, 10.8074%)

Point estimate of the true Mean moisture content = Sample mean = 9.8875%

The value 10% lies in the range (8.9676%, 10.8074%). Thus, the product meets the specifications with 95% confidence.

Given, margin of error, E = 0.1

Minimum number of tubes, n = (t * s/ E)² = (2.13 * 0.4318565 / 0.1)² = 85 (Rounding to nearest integer)