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Brittney N.

Elementary Statistics a Step by Step Approach

7 months, 1 week ago

So our question says that a random sample of 1 75 adults was given an I. Q. Test, it was found that 92 of them is called higher than 100. Based on the sample compute a 90% confidence interval for the proportion of all I. Q. Of the proportion of all adults rather whose I. Q. Are greater than 100. Then find the lower limits and the upper limits of the confidence interval. So we're supposed to carry our answer to 3 to 2 decimal places. Right? So we have a sample size end to be close to 1 75. And out of the sample size of 1 75 92 of them Actually score higher than Andre so we have 92. So that is our sample proportion pick up. It's going to be 92 Provided by 1725. So when we do the math 92 divided by 1 75, we have that to be 0.53. So to construct a 90 a 90% excuse me, a 90% confidence interval for our population. When we have the formula that says population proportion rather we have the formula says P is equals to pick up plus or minus the critical value times described it of pickup que cup divided by N. So we need to get our critical value first. Now the value of our critical value is dependent on the type of distribution that defines our dataset. So the condition for normality is that for us to use a normal distribution is based on the fact that uh if np cup is greater than or equals to five and N Q cup Is greater than or equals to five, then we can see that our dataset is normally distributed. So let's try for and pick up. So there's a 175 times 0.53. And when we do the math 1725 times 0.53, that is 92.75. Nq crap is around 75 times. So one minus 0.53. That gives us 0.47. So 0.47 times 1 75 and others are 82.25. As you can see, both values are greater than five hens. We can definitely say that our dataset is normally distributed, damages our critical value Cv is going to be is this cool? So we have a confidence level better because 2 90%. So that means our alpha level is at 10% and that is 0.10. So I'll be using a calculator to get the critical value. So I changed this to 0.10 And that was 1.6449. So we have this to be 1.6449. So let's subsist are parameters we have peace accords to 0.53 Plus or -1.6449 Times Square root 12. times zero points 47 Divided by 1 75. So P is across the 0.53 Plus or -1.6449 times. So we have the square root of 0.53 times 0.47 divided by 1 75. And that gives us 0.377. So we have a piece across 0.53 plus or minus 0.377 times 1.6449. And there are 0.06-1. So let's pick this up. We have peace across the 0.53 Plus 06-1 or we have pizza cost 20.53 minus 0.6 to one. So when we do them at pc costume, We have this to be 0.59 2 1. Or we have a piece of costume. Let's subtract that 0.4679 Questions since we leave answer into the small place. So that must be Because the 0.59 or we have P is equals to 0.47. So lower limits is 0.47. The upper limits, It's a cost to 0.59

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