Hypothesis testing for population mean.

1.      Ztest- Used when making claims about the population mean (μ) and a simple random sample is obtained.  The test statistics is the sample mean. The test is to be used under any or all of the following conditions

a.    The sample is large (n is at least 30)

The population is normal and the population standard deviation is known.

2.      Ttest - Used when making claims about the population mean of a normal or near normal population, the population standard deviation is not known, and a simple random sample of small size (n < 30) is obtained.  The test statistics is, has a t-distribution with n-1 degrees of freedom.  

3.      Paired Ttest - Used when two observation are made on the same experimental unit to investigate whether the two observations are different.

4.      Chi-Square Test - Used to compare observed distribution with an assumed distribution for fit.  It is also used to test for independence between two variables.

5.      How do you set up a decision rule for p-value and a given significant level?

6.      When is a test said to be significant?

7.      How can you use a confidence interval to test a two-sided hypothesis?  First, to test a two-sided hypothesis at level of significance α, we can construct a confidence interval based on a confidence level of 1-α.  If the null value (the value used to set of the hypothesis) is found outside the interval, then we reject H₀, otherwise we do not reject H₀.

This wine stinks.  Sulfur compounds cause "off-odors" in wine. So winemakers want to know the odor threshold, the lowest concentration of a compound that the human nose can detect.  The odor threshold for DMS in trained wine testers is about 25 micrograms per liter of wine (µg/l).  The untrained noses of consumers may be less sensitive, however.  Here are the DMS odor thresholds for 10 untrained students:

31   31   43   36   23   34   32   30   20   24

Presume that the odor threshold for untrained noses is normally distributed with? = 7 µg/l.  Is there evidence that the mean threshold for untrained tasters is greater that 25µg/l?

1.      Based on the p-value and , the null hypothesis (Ho) is

a.      Rejected

b.      not rejected

c.       Not enough information to draw a conclusion

2.      Based on the above analysis (p-value and), we conclude that

a.      The mean threshold for untrained tasters is greater than 25

b.      The mean threshold for untrained tasters is not greater than 25

c.       We do not have enough information to draw a conclusion