A biology student wishes to assess the amount of calories in a certain brand of chocolate energy bars. A sample of bars is taken and the calories are 254, 305, 206, 550, 234, 451, 327, 234, 342, and 400 calories. Find a 90% confidence interval for the mean calorie content of this brand of energy bar, assuming an approximate normal distribution. Calculate the width of our interval and discuss whether or not our knowledge about is accurate?

Construct an upper 99% bound for the mean calories in the certain brand of chocolate energy bars for above given question . Explain what the bound means

[QUOTE=pankti_ptl;166436]A biology student wishes to assess the amount of calories in a certain brand of chocolate energy bars. A sample of bars is taken and the calories are 254, 305, 206, 550, 234, 451, 327, 234, 342, and 400 calories. Find a 90% confidence interval for the mean calorie content of this brand of energy bar, assuming an approximate normal distribution. Calculate the width of our interval and discuss whether or not our knowledge about is accurate?

If you meant 330.3 +/- one sigma for 90%, then no, that's incorrect since that only
covers 68% of the area (68% confidence level, not 90%). However, +/- one
sigma might be what the question means by "width of interval". It's unclear
to me.

You are asked if our knowledge is accurate. I was struck by the 550 data item
which sticks out like a sore thumb. So I did two plots of the PDF, one for the
data as given (white curve) and one with the 550 changed to 400 (blue curve).

The effect of the "sore thumb" on the variance and thus the on width of the bell
curve is enormous, as you can see. I think far more data needs to be collected
before we could claim "sufficient knowledge" (to create confidence levels we could
have any confidence in).

BTW, the SUMs are of all the PDF values from 0 to 1200. Notice that the white
curve left tail doesn't reach zero at X = 0 (left origin). This is reflected in a
small effect on the SUM for that plot (SUMs should equal 1). That sort of thing
can be handled but it's good to be aware of it.