Question

the wall thickness of 21 randomly selected glass 2-liter bottles was measured by a quality-control engineer. the wall thickness of those glass 2-liter bottles follows a normally distribution with unknown variance. the sample mean and the sample standard deviation of those 21 selected bottales was found to 4.15 millimeters and 0.09 millimeter, respectively. which of the following is the correct 90% two-sided confidence interval for the mean wall thickness?

Answer 1

The 90 % Prediction interval on the wall thickness of next bottle tested is (4.41, 4.99).

What is meant by Prediction Interval?

A prediction interval is a form of confidence interval (CI) used with regression analysis predictions; it is a range of values that forecasts the value of a new observation based on your existing model.

Confidence intervals and predictions are frequently used interchangeably. They are not exactly the same thing, though.

A confidence interval is a set of values connected to a population parameter. the population's mean, as an illustration.

Where you anticipate an upcoming number to fall is called a prediction interval.

The Interval Uncertainties

It doesn't imply that you can forecast with confidence where a single number will fall, just like with most things in statistics.

Confidence intervals are usually accompanied with a confidence level, which represents the amount of uncertainty.

How to solve?

X=4.7

s=0.7

n=25

The tabulated value of t at 24 degree of freedom is 2.06

t24=2.064

The 90 % Prediction interval on the wall thickness of next bottle tested is given by:

=(4.7±t24×0.7√25)

=(4.7−2.064×0.75,4.7+2.064×0.75)

=(4.7−0.28896,4.7+0.28896)

=(4.41,4.99)

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