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danny89

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Dec 11, 2005
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1. The following data set shows the number of customers a fast-food restaurant served over a 49-day period during lunchtime (11:00 am to 2:00 pm). Find the 95% confidence interval for the mean.

388 246 339 309 205 330 357
360 235 255 305 340 301 303
361 248 359 223 352 329 260
331 325 350 332 249 320 250
268 329 246 338 224 305 319
239 306 201 343 208 275 280
313 344 347 356 257 342 328


Things I need to know: the formula used and how to computer it. I also have trouble finding the value on the t table or z table
 
G'day, Danny.

Which formula are you referring to?

The mean: add up all the numbers and divide by the 49 (there are 49 numbers).

The standard deviation formula from a Google search is here.

But I much prefer the form
\(\displaystyle \L \sigma^2 = \frac{\sum x^2 - n(xbar)^2}{n}\)
and take square roots to get the standard deviation. n is the number of numbers, here 49; x-bar is the mean of the sample; \(\displaystyle \sum x^2\) means to sum the squares of the data. A frequency table could make things quicker if there were a few repeating digits, but it doesn't look like it.

This is very tedious. If you have a suitable calculator or Excel, use it. Copying & pasting into Excel is always nice.

Or do you need to know the formula for a confidence interval of the mean:
\(\displaystyle \L xbar - Z.\frac{\sigma}{\sqrt{n}} < \mu < xbar + Z.\frac{\sigma}{\sqrt{n}}\)

A 95% confidence interval means 0.95 probability of a sample having a mean in that interval, so the area of concern of a bell curve is 0.475 either side of the mean. The corresponding Z-score from the tables is 1.96 .
 
Okay so I was given this formula to use just checking to see its the same:

the mean plus or minus is equal to z number times s over n square root:
i have found the mean which is 300.6122, z number is 1.86 , and n= 49, and s which I'm assuming is the STD= 49.05. So:

300.6122 plus or minus 1.96 (49.05/square root of 49)

is this right?[/code]
 
One question I have in correspondance with the z score, how do you know how to look it up on the table? I know you look at the confidence interval, but then what?
 
danny89 said:
One question I have in correspondance with the z score, how do you know how to look it up on the table? I know you look at the confidence interval, but then what?
Click to expand...
It's just like an inverse normal distribution problem. Look in the standard normal distribution table for the number 0.4750. This comes from 0.95/2=0.4750 and re. my post above.

0.4750 is bang on a Z-score of 1.96. If you are unfamiliar with using the standard normal distribution table, check with your textbook. This should have been covered before you tackled confidence intervals.
 
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