Exercise 9 uses μ=189 lb, which is based on Data Set 1 "Body Data" in Appendix B. Repeat Exercis

step 1 This problem relies on information from a previous problem. It's referring you back to problem n

Exercise 9 uses μ=189 lb, which is based on Data Set 1 "Body...

Key Concepts

Bias Introduced by Outdated Information

When an outdated mean is used in an analysis, it introduces bias—a systematic error that distorts the results. This bias can lead to underestimating or overestimating key metrics, thereby misinforming decision-making. Recognizing and correcting for such biases is essential in statistical analysis to maintain the integrity and reliability of the conclusions drawn from data.

Mean as a Measure of Central Tendency

The mean is a fundamental statistic that summarizes the central location or average of a dataset. Its accuracy is critical because many analyses depend on comparing individual measurements or group averages to the mean. When an outdated or incorrect mean is employed, the overall interpretation of the data can be skewed, leading to incorrect conclusions about the underlying population.

Parameter Assumptions in Statistical Models

Statistical models often rely on fixed parameters, such as predetermined mean values, to make predictions or inferences. Using an outdated parameter value can affect the validity of the model, leading to systematic errors. This highlights the importance of continually updating parameter assumptions with current data to ensure that the model accurately reflects the true characteristics of the population.

Transcript

00:01 This problem relies on information from a previous problem.

00:06 It's referring you back to problem number nine, and just in case you were not with me on the solution of that problem, i'm going to take you back through some of the information from that problem as well.

00:19 So in the previous problem, we had an elevator, and it had a load capacity of 4 ,000 pounds, and there was a safety net built in, a 25 % safety net, that if you take 25 % of 4 ,000, you'll get 1 ,000, we added on.

00:39 So even though it was saying that it can hold 4 ,000 pounds, it technically could hold 5 ,000 pounds because they've built in that safety net.

00:49 Also in the previous problem, we were talking about putting 27 adult males into that elevator.

00:57 So if we take those 27 adult males and divide it into the 5 ,000 pound capacity, we can average at about 185 pounds per male and still meet the requirements or the maximum capacity of that elevator.

01:18 There was also some other assumptions.

01:20 The other assumptions was that male weights were normally distributed.

01:43 We also had an assumption that the average male weighed 189 pounds, and the standard deviation was 39 pounds.

01:53 So now we're ready to start number 10 with some adjustments to this data.

02:01 So in problem number 10, it's asking us, instead of using an average of 189, they want us to use a lower average for an adult male weight at 174 pounds.

02:16 And we are repeating exercise 9, and exercise 9 was asking us to determine what was the probability that when we put these 27 males into the elevator, we were overloaded.

02:32 Well, that means then the average of those 20s, was exceeding the 185 pound that we got up here.

02:43 So in order to solve this problem, we are going to have to talk about information about a sample.

02:51 We are using a sample of 27 males, so the sample size is 27.

03:00 We will need to determine the average of our sample means, and we will need to determine the standard deviation of our sample means.

03:13 So the average of our sample means is going to be mu subx bar, and the standard deviation is going to be sigma subx bar.

03:23 And the central limit theorem will help us to evaluate those two statistics, and the average of the sample means, according to the central limit theorem, will be equivalent to the average of our population, and the average of our population, in this case, is 174 pounds.

03:45 And the standard deviation of our sample means will be equivalent to the standard deviation of our population divided by the square root of our sample size, and in this instance, it's going to be 39 divided by the square root of 27.

04:03 Now, in order to solve our problem, we are going to draw our bell -shaped curve, and we can do that because they told us that male weights had normal distribution.

04:17 We are going to put the average in the center, so that's where we got our average from.

04:26 And we are asked to determine what's the chances or what is the probability that the average male that's getting in this.

04:35 Elevator weighs more than 185 pounds.

04:41 We are going to need to utilize our z score formula to solve it...

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