Hypothesis Testing?

[yadvinders]

The Hudson Valley Bottling Company distributes root beer in bottles labeled 32 ounces. The Bureau of Weights and Measures randomly selects 50 of these bottles, measures their contents and obtains a sample mean of 31.80 ounces with a standard deviation of 0.75 ounces (assume population values for mean and standard deviation). Using a 0.01 significance level, test the Bureaus claim that the company is cheating consumers. Indicate whether you would use a z score or t score, give the value of that score and the critical value to 2 decimal places, and state whether you "Reject" or "Fail to Reject" the null hypothesis. Example Answer: t, 1.45, 3.12, Reject

[Pirates0154]

Since the values given are for the population, we use a Z test. You would use a T test for one where the standard deviation of the population is unknown.

The equation for the Z is:

Z = x - u / (s / sqrt(n))

where x is sample mean, u is the population mean, s is standard deviation and n is sample size. Plug in 31.8, 32, .75, and 50 respectively: Z = -1.88

The Z* can be found using the Z chart. The calculator is faster: Z* = InvNorm(.01) = -2.32

We fail to reject the null hypothesis because |Z| < |Z*|

In total: Z, -1.88, -2.32, Fail to reject