math probability

Question

You measure 46 textbooks' weights, and find they have a mean weight of 37 ounces. Assume the population standard deviation is 2 ounces. Based on this, construct a 99% confidence interval for the true population mean textbook weight. Round answers to at least 4 decimal places.

Answer 1

z score for 99% = 2.576, use z tables or a z calculator

empirical rule doesn't help so much 68-95-99.7 for 1.-2-3 standard deviations from the mean, but it tells you the z score for 99 is less than 3 & more than 2, just like 2.567

CI = mean +/-z(sd)/sqr(n)

CI= 37 +/-(2.567)(2/sqr46) = 37 +/-.7570= 36.2430, 37.7570

Confidence Interval = (36.2430, 37.7570)

Answer 2

Answer 3

Hi Maggie,

Formula for this is:

CI = xbar +/- z* SE

xbar = sample mean

z* = z-critical value

SE= standard error = sigma/sqrt(n)

xbar = 37 oz.

SE = 2/sqrt(46) = 0.295

Three z-critical values are worth memorizing for any statistics class. Yes, you can get from the z-table, but that takes longer than recalling from memory. They are:

z90% = 1.645

z95% = 1.96

z99% = 2.576

Here, you are interested in 99% confidence, so:

z* = 2.576

CI = 37 +/-(2.576*0.295)

CI = (36.2404, 37.7596)

I hope this helps.