Question

An engineer is designing a nylon connector to be used in an automotive engine application. The engineer is considering establishing the design specification on a Wall thickness at 3/32 ???h but is somewhat uncertain about the effect of this decision on the connector pull-off force. If the pull-off force is too low, the connector may fail when it is installed in an engine. Eight prototype units are produced, and their pull-off forces measured (in pounds):

12.6, 12.9, 13.4, 12.3, 13.6, 13.5, 12.6, 13.1

(01) The population is:

a. All nylon connectors that will be used in the automotive engine application

b. Pull-Off force of the nylon connectors used in the automotive engine application

c. Eight prototype units of nylon connectors produced for experimental purposes

(02) The sample is:

a. All nylon connectors that will be used in the automotive engine application

b. Pull-Off force of the nylon connectors used in the automotive engine application

c. Eight prototype units of nylon connectors produced for experimental purposes

(03) The Sampling Design is:

a. Observational; Simple Random Sample

b. Experimental; Completely Randomized Design

c. Experimental; Matched Pairs Design

(04) The response variable is:

a. Pull-Off force; Quantitative Random Variable

b. Wall Thickness; Quantitative Random Variable

c. Design Parameters (Categorical) with two levels; Pull-off force, Wall thickness

(05) The critical value that should be used by the engineer in order to construct a 95% Confidence Interval for the true Pull-Off force of the 3/32 ?? nylon connector is

a. 1.65

b. 1.96

c. 2.36

(06) The engineer wants to decide the required sample size in order to estimate the 95% ?????????? ???????? for the true mean Pull-Off force of 3/32 ?? nylon connectors with an error level of 0.25 ?????? or less. However, this calculation is not possible, since ? (standard deviation of the Pull-Off force of 3/32 ?? nylon connectors) is unknown. Therefore, the engineer decided to assume ? = 0.45 ?????? only for the sample size calculation. What should be the calculated sample size?

a. 4

b. 12

c. 13

Answer 1

## Question : An engineer is designing a nylon connector to be used in an automotive engine application. The engineer is considering establishing the design specification on a Wall thickness at 3/32 ???h but is somewhat uncertain about the effect of this decision on the connector pull-off force. If the pull-off force is too low, the connector may fail when it is installed in an engine.

Eight prototype units are produced, and their pull-off forces measured (in pounds):

12.6, 12.9, 13.4, 12.3, 13.6, 13.5, 12.6, 13.1

## (1) The population is:

correct option is = b. Pull-Off force of the nylon connectors used in the automotive engine application

## (2) The sample is:

correct option is = c. Eight prototype units of nylon connectors produced for experimental purposes

## (3) The Sampling Design is:

correct option is = a. Observational; Simple Random Sample

## (4) The response variable is:

correct option is = b. Wall Thickness; Quantitative Random Variable

## (5) The critical value that should be used by the engineer in order to construct a 95% Confidence Interval for the true Pull-Off force of the 3/32 ?? nylon connector is

correct option is = c. 2.36

( use t statistical critical table ) here df = 8-1 = 7 and two tailed test used for critical vlaue

## (6) The engineer wants to decide the required sample size in order to estimate the 95% ?????????? ???????? for the true mean Pull-Off force of 3/32 ?? nylon connectors with an error level of 0.25 ?????? or less. However, this calculation is not possible, since ? (standard deviation of the Pull-Off force of 3/32 ?? nylon connectors) is unknown. Therefore, the engineer decided to assume ? = 0.45 ?????? only for the sample size calculation. What should be the calculated sample size?

n = (critical value ^2 * population standard deviation ^2) / margin of error ^2

here critical value is = 1.96 here we have to use z critical table .

standard deviation is = 0.45 and

margin of error = 0.25

n = ( 1.96^2 * 0.45^2 ) / ( 0.25 ^2)

n= 12.4467 ie approximately 12

correct option is = b. 12