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The number of megapixels in a digital camera is one of the most important factors in determining picture quality. But, do digital cameras with more megapixels cost more? The following data show the number of megapixels and the price (S) for 10 digital cameras (Consumer Reports, March 2009 ).$$\begin{array}{l}{\text { a. Use these data to develop an estimated regression equation that can be used to predict }} \\ {\text { the price of a digital camera given the number of megapixels. }}\end{array}$$$$\begin{array}{l}{\text { b. At the } .05 \text { level of significance, are the number of megapixels and the price related? }} \\ {\text { Explain. }}\end{array}$$$$\begin{array}{l}{\text { c. Would you feel comfortable using the estimated regression equation developed in }} \\ {\text { part (a) to predict the price of a digital camera given the number of megapixels? }} \\ {\text { Explain. }}\end{array}$$$$\begin{array}{l}{\text { d. The Kodak Easy Share } Z 1012 \text { IS digital camera has } 10 \text { megapixels. Predict the price }} \\ {\text { of this camera using the estimated regression equation developed in part (a). }}\end{array}$$

a. $\hat{y}=-145.027+38.319 x$b. Reject the null hypothesis $H_{0}$ or significantc. Yesd. $\$ 238.163$

Intro Stats / AP Statistics

Chapter 12

Simple Linear Regression

Linear Regression and Correlation

Piedmont College

Cairn University

Oregon State University

Idaho State University

Lectures

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04:56

Digital Camera Prices The …

02:03

Digital camera. A company …

03:15

Developing Digital Photos<…

01:59

Suppose that Smartphone A …

03:11

CAMERAS For Exercises 25 a…

03:27

Human vision normally cove…

00:42

Total Profit. When $x$ hun…

04:53

$\cdot$ A certain digital …

00:27

The major advantage CCDs h…

05:39

A camera company estimates…

00:32

Low-resolution digital pho…

00:53

A good quality camera &quo…

01:36

03:14

(II) Human vision normally…

01:10

The focal length $f$ of a …

02:31

00:30

Use the following informat…

01:04

The average price of a dig…

The resolution limit of a …

03:12

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

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