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The prices (in dollars) for & particular model of digital camera with 6.0 megapirels and an optical 3X zoom lens are shown below for 9 online retailers Round sa...

Question

The prices (in dollars) for & particular model of digital camera with 6.0 megapirels and an optical 3X zoom lens are shown below for 9 online retailers Round sample statistics and final answers to one decimal place_192 189 249 25 214 201 221 180 200Douload dataEstimate the true mean price for this particular model with 95%0 confidence_ Assume the rariable is normally distributed:

The prices (in dollars) for & particular model of digital camera with 6.0 megapirels and an optical 3X zoom lens are shown below for 9 online retailers Round sample statistics and final answers to one decimal place_ 192 189 249 25 214 201 221 180 200 Douload data Estimate the true mean price for this particular model with 95%0 confidence_ Assume the rariable is normally distributed:



Answers

Digital Camera Prices The prices (in dollars) for a particular model of digital camera with 18.0 megapixels and a $f / 3.5-5.6$ zoom lens are shown here for 10 randomly selected online retailers. Estimate the true mean price for this particular model with $95 \%$ confidence. $$ 999 \quad 1499 \quad 1997 \quad 398 \quad 591 \quad 498 \quad 798 \quad 849 \quad 449 \quad 348 $$

For this problem were given 10 different camera prices and were asked to estimate the true mean price of these cameras. So I have written down all 10 prices and we're going to start this problem by calculating the mean and standard deviation. Recall that the mean is calculated using some of all the numbers divided by and or the number of data points. And that's equal to your mean. Your standard deviation is calculated using this formula where you would take their route of your difference is whole over and not minus one. Of course, you can do this by hand if you so choose. But I have taken the liberty of using my calculator, which I recommend you do as well. And you should get 8 42 0.6, as you're mean and around 5 34 0.3 has your standard deviation. So with this information, the next thing we're going to do is get our T value. Recall that in order to find our t value, we need two components are degrees of freedom and our confidence level. Me actually draw a line here. So you know that this is for a different thing. Our degrees of freedom for this problem is just gonna be end minus one, just like it always is. So the 10 prices minus one which equals nine and our confidence level were provided is 95%. Now use your teases a sig table in the back of the book. Finally, two degrees of freedom nine confidence level of 95. The resulting T value should be 2.26 If you need help with this, go back to an earlier problem. I believe it's number three and there's an explanation. Um, so now that we have our tea value, we have our me and and we have our standard deviation. Let's create our confidence interval. So the formula for the confidence interval is as follows. You have your mean and you're going to say, plus or minus your t value times standard deviation over the square root event. So let's plug in what we have. For that. We know that our mean waas 8 42.6 plus or minus her T value, which is 2.26 times, are square root. Our times are standard deviation, which is 5 34.3 all divided by the square root of total numbers, which is 10. I'll give you a minute to plug that into your calculator. Be sure to be careful with your parentheses when you're doing this. Um, this step in particular can get very nasty if you're not using parentheses in the right way. It's a very commonplace for algebra errors. Um, and then once you figure out this whole term, add it to 8 42 and subtracted from 8 42 and you will get the range of values, so hopefully you're almost there. If not, feel free to pause as needed. But your answer should be for 60 0.7, less than or equal to new, less than or equal to 12 24 0.45 So this is our final answer right here. And if you're asked to explain this, we can say that we are 95% confidence that the true mean will be somewhere in between this range or in other words, if we were to sample repeatedly, 95% of the time are true, mean would fall within this range

80 two different mind. The critical value for table six degrees of freedom is on minus one, which is 11 minus one, so it's equal to 10. So the chi square off one minus alfa over to is able to 4.865 and the chi square of all for over two is equal to 15.987 So the boundaries for the standard deviation is the square root of n minus one over X squared off Alfa over to times of thunder deviation, which is equal to 86.2 or seven, and the square root of n minus one over chi square off one minus off over two times. Standard deviation is equal to 156.273 eso the boundaries for the variance, which is the square off the number off the standard deviation. So the variance is, um, the square value off these values so is equal to seven for one 3.647 and 244 to 1.251

Number 20. So the critical value from table six off degrees of freedom, then minus one, which is 29. So the chi square off one minus Alfa is equal to 17.7 or eight and the chi square off also is 42.557 The boundaries for the standard deviation. Eyes equal to the square. Root off n minus one over chi square off Alfa over to times as 30 minus 1/42 300.557 Time 3600 which approximately equal to 297 1.78 and other boundaries in minus one over X square or pie square minus off over two times. Yes, which is 30 minus 1/17 300.708 Time 36 years You. So this is approximately equal. 24606.98 The bombers for the variance will be the square value off these values, which is 8831476 and 212 to 4 to 65

For this question we've been given. Our sample size is 20. This means our degrees of freedom would become 19. Since we're finding a 90% confidence in terrible R L four becomes 3.1 and others were given the samples. You can confirm it the sample standard deviation Using this formula here on, if you calculated, you'll see that our sample standard deviation for this question is 20.2844 Not every found these values. We can find the critical values using the G table, the critical values we find archives for alphabet toe guy square one minus out of it. That's for Alphabet. Do in our case would become guy scores 0.5 with decrease of freedom 19 If you didn't g table, this value comes to 30.144 chi square one minus a little By doing our case would be guys for a 0.95 with degrees of freedom 19. If you take the G table, this value is 10.117 Other reformed the critical values. We can move on to calculating the confidence interval for population variance. We used this expression here to calculate the populate, the confidence interval for population variance. So see, duping the values we have in the expression we get this expression here simplifying this expression further we get the lower boundary off our confidence interval for the stand off the population variance as 259.3445 and the upper boundary is 772.727 Now that we found the confidence interval for population variance, we can use that to calculate the confidence interval for our standard deviation. To do so, we take the square root off the confidence in government we found for the population variance taking squaring off the confidence interval for a population variance we get this year and simplifying it further, we get the lower limit for our conference and terrible for this population standard deviation A 16.1042 which is square root off 259.34 or five and the upper limit is 27.7980 which is the square root off 772.7%. So this here is how we calculate the confidence interval for the population variance on the population standard deviation


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