Stage 1: Image Emulation.
I wondered why an image taken on a 10 Megapixel camera did not have a file size twice the size of one taken with a 5 Megapixel camera so I decided to conduct a few Image size experiments to try and find an answer to this question. The following tries to explain what I did and what results were obtained...

The first task was to import an image from the 10 Megapixel camera on to the PC and look at the properties of the file so I could apply similar attributes for new images created in Paint Shop Pro 7 to give the best representation of a picture taken with the camera. The main points being 72 dpi, 24 bit (16.7 million colours) and the dimensions of the image 3648 x 2736 pixels.

Having obtained these values I created a New file in Paint Shop Pro 7 and coloured it with a single colour, (black for this instance) and saved it in the programs native uncompressed format (.psp) to give a standard base image from which to work from every time. I then saved the same image this time as a .jpeg file using standard encoding at the lowest compression setting, (factor 1) in the Save Options dialogue box.
The file size for this image was found to be 152KB.

The next task was to create an image using the same method only this time to represent an image taken with a 5 Megapixel camera hence the image dimensions are 2592 x 1944 pixels this time. This was saved in the programs native format like before. Then the image was saved as a .jpeg file with the same compression factor as before. The file size for the new image file was found using the properties dialogue box.
The file size for this image was found to be 77.8KB.

The next part of the experiment was to take the original 3648 x 2736 pixel .psp image and resize it to represent the 5 megapixel size, (2592 x 1944 pixels) using the resize tool in Paint Shop Pro 7. This was again then saved as a .jpeg file using the same attributes as before and the image file size found using the image file properties dialogue box.
The file size for this image was found to be 77.8KB.

So far the experiment had been on a single colour and it was found that whatever the single colour was (Black, White, Red, Blue, Green etc.) the file size was always the same, (152KB and 77.8KB respectively).
The next phase was to conduct the previous stages of the experiment using various two colour, (black & white, Blue & Red) images. The file size changed but not to any great extent. For the Black & White image The file size was found to be 153Kb for the 10 Megapixel image,and 78.4KB for the 5 Megapixel image. For the Blue & Red image the file sizes where slightly higher again being 155KB and 79.4KB for the respective Megapixel image.

The final part of this test was to create a multi coloured image using the whole colour range from Paint Shop Pro 7 basic colour palette and then repeating the previous resizing and .jpeg saving methods for both of the Images representing the 10 Megapixel image and the 5 Megapixel image. This time the file sizes turned out to be significantly different.
For the 10 Megapixel image, The file size was found to be 416Kb and for the 5 Megapixel image, The file size was found to be 294KB.

Stage 2: Actual Camera Images.
For the next part of the experiment I planned to compare image file sizes taken with the Sony Cyber shot DCS-W170s camera using the 10 Megapixel setting and the 5 Megapixel setting that is part of the cameras quality options to see what relative difference it made. To make sure I got the best accuracy whilst switching between settings I used a tripod to fix the position of the camera, kept the camera in "Auto" and used the 2 second timer to eliminate camera shake for each picture so as to keep a constant for each image.

I took numerous pictures of flowers and plants that were available to me in my garden and chose the best four for comparison, I tried to get a variation in the amount of colours used to see what difference it would have on the file size using the cameras built in .jpeg compression factor.
The file sizes were found to be as follows:-

Conclusion:
From the experiments conducted with Paint Shop Pro 7 and the Sony Cyber shot DSC-W170s camera it appears that the more colours that are evident in the captured image the better the .jpeg compression algorithm works to reduce the file size.
If a single colour is present a 10 Megapixel image is roughly twice as big as a 5 Megapixel image, this does not mean that the image quality is twice as good, just bigger! A multi coloured 5 Megapixel image using all the basic colours tends to be about 70% of a 10 Megapixel image.
File compression appears to dependent on what colours are used are used in the image as well, (see Black & white, Blue & Red examples above) although the significant difference in file size seems to be negligable.
Having conducted these experiments I am satisfied now that although my new camera is a 10 Megapixel model the file size is not necessarily going to be double that of a 5 Megapixel camera to produce better photographs!