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It is generally believed that electrical problems affect about 14% of new cars:. An automobile mechanic conducts diagnostic test on 128 new cars on the lot:Where do...

Question

It is generally believed that electrical problems affect about 14% of new cars:. An automobile mechanic conducts diagnostic test on 128 new cars on the lot:Where do we expect the sampling distribution to be centered?What is the standard deviation of the sampling distribution? Show your work! What is the probability that in this group over 18% of the new cars will be found to have electrical problems? What is the z-statistic for this sample? Show your work!Draw or copy the distribution. What is t

It is generally believed that electrical problems affect about 14% of new cars:. An automobile mechanic conducts diagnostic test on 128 new cars on the lot: Where do we expect the sampling distribution to be centered? What is the standard deviation of the sampling distribution? Show your work! What is the probability that in this group over 18% of the new cars will be found to have electrical problems? What is the z-statistic for this sample? Show your work! Draw or copy the distribution. What is the p-value for this sample? Indicate the p-value on the graph:



Answers

Identify the indicated values or interpret the given display. Use the normal distribution as an approximation to the binomial distribution, as described in Part I of this section. Use a 0.05 significance level and answer the following: a. Is the test two-tailed, left-tailed, or right-tailed? b. What is the test statistic? c. What is the $P$ -value? d. What is the null hypothesis, and what do you conclude about it? e. What is the final conclusion? In a TE Connectivity survey of 1000 adults, $29 \%$ said that they would feel comfortable in a self-driving vehicle. The accompanying StatCrunch display results from testing the claim that more than $1 / 4$ of adults feel comfortable in a self-driving vehicle.

The problem deals with car company that is interested in the lifetime of its disk brake pads. So first thing we're gonna look at is the population data for the lifetime of this quick. And they tell us that it follows the normal curve and we know that the population means ist $5.55,000 miles. And we know that the standard deviation is 45 100 miles. So I'm gonna put that fear and the standard deviation is going to be this distance. So I know my standard deviation is 4500 miles. They want to test out some new brake pads and they take a simple random sample of a cars that have these new brake pads. And that lets me know that I have a sample size of eight. And if I take that sample size of eight and I figure what their lifetime is, and then I divide by eight, I'm going to have the mean of that sample. So this stance for the mean of one sample and part A that it has the same lifetime distribution as the previous type of brake pads and it wants to know the same play distribution for the sample's for all the samples. So over here on going to ride the sampling distribution of the sample mean the folk art A. This is gonna be the same plane distribution of the sample means. So one thing I know about a sampling distribution of means is that the means are less variable than individual observations. So this is gonna also follow a normal curve. But this normal curve is going to be a little more normal than the population. Data is gonna be a little more normal. And we know that our population mean is the same thing as our sampling distribution means. So I'm gonna know that like this, and I also know that is 5,555,000. Now I need to figure out the standard deviation. So to find a danger deviation of the sampling mean I have to put the danger deviation of the population over the square root of the sample size. The standard deviation of my population here is 4500 divided by square root of my sample size on my sample size with age. So that's going to give me a standard deviation of 1591. So my standard deviation, if you notice it's a lot smaller than what it was in the population data. So I'm gonna have these two as one standard deviation and my standard deviation is going to try a year. And that distance standard deviation of the sample means is 1591. So in part B, they find one of the the mean of one of the samples, and it turns about it turns out to be 51,800 miles and in part B. They're asking me to find the probability that the sample mean lifetime is 51,800 miles. Word left. So I'm looking for the probability that the sample mean lifetime listener equal to 51,000 800. So if I'm looking at my graph of a year of my sample means 1800 is probably somewhere like years. So this is 51,000 read hunters, and I need the probability would be the area under the curve from this point over. So the first thing I need to do is to figure out what is the standard deviation with this, the final standard deviation I have to find the Z score. The easy score is equal to the value of your looking for 51,800 minus your means that C 5000 divided by your standard deviation 1591. So my score is equal to negative 3200 divided by 1591 and that's equal to negative 2.1 So if I need to find that proper boat probability in green, I have to go to a Z tables to look up. What the probability is the area under the curve beard green. So I'm looking for the probability that they less than or equal to negative 2.1 So if I go to my probability tables and I have negative two point, you're a 0.1 I get the answer to be 0.2222 So this is going to equals zero point you wrote to to to. And that's also the probability that means is less than or equal to 5100 51,800. So what? That means that there's a approximately a 2% chance that the mean of a sample falls in this great screen area.

So in this question, we're told that cars arrive at Burger King's at the reduction 20 cars per hour. And we have a random sample of 40 one hour time periods, Which has 22.1 as the mean, and Yep, which has trying to appoint one is the mean number of cars arriving. Now. First we're asked what the samp, why the sampling distribution of X is approximately normal, so Sampling distribution is approximately normal because our sample size is 40, which is more than r equals 2 30. So according to the central limit theorem normality Holtz, So that's our answer to part A. Now in part B were asked for the mean and standard deviation of the sampling distribution of fixed, assuming the population mean and standard deviation. So the mean Is the population mean, which is 20. And then our sampling the standard deviation of the sampling distribution is basically the population. Standard deviation over the sample square root of the sample, which is approximately .707. So we have our answer to part P. When part C were asked what the probability, what is it called? The simple random sample of 40 One hour time period results in a mean of at least 22.1 cars of probability That our sample means is more than r equals to 22.1. So we have our sample standard deviation and sample means. So probability here we convert this to the Z distributions as quality sees more than equals to 2.97, which is one minus the probability easy. You see less than 2.97, Which is equals two .0015. So that's our answer to see. Is this result unusual? Well, it's a very low probability, so, yes, it is unusual, and what might be concludes what we might conclude is that this random sample actually has the mean higher, Yeah. 20 because it is an unusual result.

First here. We want to determine whether or not we have a probability distribution. Since the some of the probabilities is one, we do in fact have the probability distribution. And so to find our mean, otherwise knows are expected value. We take zero times a probability of zero, which is 00.358 plus one times the probability of one which is 10.439 also two times the probability of to this 0.179 plus three times the probability of three 0.24 And so whenever we add these up, this gives us Armenia's 0.86 nut. So that is our meat going to find the standard deviation needy of X squared first. And so this means we take zero squared times 0.358 plus once word 1.439 plus two squared. I was 0.179 plus three squared was to four. And so we evaluate this and this tells us that he have X squared is 1.371 Yeah, it's our standard deviation. Sigma is equal to the square root of evac square minus G of X square, which is route 1371 minus 0.869 squared the spirit of 1.371 minus point 869 Spartan gives us approximately 0.7 84 eight, and so that is our standard deviation.

Brought him 17 number off sample is equal to 14. Sample standard deviation in 3.9. The confidence clever is a 0.299 and the alpha is one minus C over to which is over four or five. So the critical value from the table off the high school distribution extra square off one liners, all for over two is 3.565 on Chi square, off over two is equal to 29.8 819 The boundaries off the confidence. Confidence in the interval for the standard deviation is, uh, end minus one over chi square off Alpha over two times s, which is 2.5751 and the other boundary in minus one off Chi Square for minus all over two times asked equal to 7.4474 eso The boundaries for the variance is the square off this value, which is 2.5751 square 7.4474 squared, which is 6.631 and 55.46 14


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