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13. Rob is a quality control specialist at a toothpaste factory. Part of his job is to verify that the filling machines are dispensing the proper amount of toothpaste into each tube. It is his first day working on a new machine that fills travel size toothpaste tubes.

The machine is supposed to produce an average fill rate of 0.85 ounces of toothpaste per tube.

: Rob randomly samples 16 of the 1000 travel size tubes of toothpaste that the machine produces that day. The weight, in ounces, of Rob's sample data is presented in the stem-and-leaf plot below. The stems are tenths of an ounce and the leaves are hundredths of an ounce.

13 Rob is a quality control specialist at a toothpaste factory Part of his job is to verify that the filling machines are dispensing the

Answer :

Rob's one-sample t-test decision is justified. The sample size is appropriate, the sample is random, and conditions for normality are likely met based on the sample size.

Rob's decision to use a one-sample t-test should be justified based on the conditions for performing such a test. Let's evaluate the given statements:

The 10% condition is not met.

This condition typically applies to the population size when using the Central Limit Theorem, and it's not directly relevant for a t-test. The focus is on the sample size, not the population size.

The Normal/Large Sample condition is not met.

The sample size for a one-sample t-test should be large enough for the sampling distribution of the mean to be approximately normal. With a sample size of 16, this condition is generally met.

The 10% condition is met.

As mentioned earlier, the 10% condition is not particularly relevant for t-tests.

The sample was random.

Rob mentions that he randomly sampled 16 tubes, satisfying the random sampling condition for a t-test.

The sample is not random because it came from one machine.

The fact that the sample came from one machine does not necessarily violate the random sampling condition. Random sampling means that each tube has an equal chance of being selected, which is plausible in this scenario.

The sample data contain no outliers.

Outliers can impact the results of a t-test. However, the presence of outliers should be assessed using appropriate tools, and it is not explicitly mentioned in the stem-and-leaf plot.

The Normal/Large Sample condition is met.

Given the sample size of 16, the Normal/Large Sample condition for a t-test is considered met.

The sample data contain at least one outlier.

The presence of outliers is not explicitly addressed, so it cannot be concluded that there is at least one outlier.

In summary, Rob's decision to use a one-sample t-test is generally justified. The sample size is reasonable for the t-test assumptions, and the conditions related to random sampling and normality are likely met.

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