#2. a) When you construct the confidence interval, where does the sample mean stand compared to the interval?
b) In which interval would you have more confidence (probability): a narrow one or a wide one?
#4. We know that the population is ND(µ, 3.0).
a) Since σ is known, we use the formula X-bar ± z*σ/sqrt(n). Plug in the given information and calculate! (Remember: the z-value comes from the z-table, and it's the z-score that traps the appropriate amount of area in the middle of the bell. So, for this one, we must trap the middle 95% area, which means we need 5% outside the interval and evenly split between top & bottom. So the z-scores must chop off the bottom 2.5% and the top 2.5%.)
#32. Since σ is unknown, we use the formula X-bar ± t*s/sqrt(n). Plug in the given information and calculate!
#33c. Same hint as for #32, but you will need to calculate the X-bar & s values.
Here's a bonus for looking here: X-bar = 438.3 and s = 15.1.
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