An automated filling machine is used to fill bottles with liquid detergent. A random sample of 20 bottles results in a sample variance of fill volume of s2 = 0.0153 (fluid ounces)2. If the variance of fill volume exceeds 0.01 (fluid ounces)2, an unacceptable proportion of bottles will be underfilled or overfilled. Is there evidence in the sample data to suggest that the manufacturer has a problem with underfilled or overfilled bottles?

An automated filling machine is used to fill bottles with liquid detergent. A random sample of 20 bottles results in a sample variance of fill volume of S² = 0.0153 (fluid ounces)². If the variance of fill volume exceeds 0.01 (fluid ounces)², an unacceptable proportion of bottles will be underfilled or overfilled. Is there evidence in the sample data to suggest that the manufacturer has a problem with under filled or overfilled bottles? Use α = 0.05, and assume that fill volume has a normal distribution

This implies that there is no problems in incorrectly filled because there weren't strong to sustain the there is a problem

Explanation:

Using hypothesis test can come in handy for to measure and accept the real variance and standard deviation of a population distribution

Following the eight steps procedure would guide;

1. Identify the parameter of interest is the population : Variance denoted as S²

2. Formulate the Null hypothesis

H° ;S² = 0.01

3. Draw an alternate hypothesis H¹: S² > 0.01

4.α = 0.05

5. Use Chi ² Test.

The test statistic is:

where is the following

explanation:

answer: semi-infinite solid initially at a uniform temperature of 400 ◦c is cooled at its surface by convection. the cooling fluid at a constant temperature of 200 ◦c has a convective coefficient (ha) of 250 w/m2.k. the physical properties of the solid: k = 20 w/m.k and α = 4 * 10-5  m2/s. using δx = 0.04 m and δt = 10 s. write the finite difference equations describing the transient heat transfer of the first five δx and the temperature profile after 30 s.