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Using a Confidence Interval to Test a Hypothesis ( Unknown)

 

 

Example: In order to test   versus   a simple random sample of size  is obtained from a population that is known to be normally distributed.

 

(a) If   and  compute the test statistic.

 

(b) Draw a t-distribution with the area that represents the P-value shaded.

 

(c) Approximate and interpret the P-value.

 

(d) If the researcher decides to test the hypothesis at the  level of significance, will the researcher reject the null hypothesis?  Why?

Test the hypotheses:    vs.    The underlying population is known to be normally distributed.  The sample statistics are = 18.3,  s = 4.3 and  n = 18.  Press STAT, highlight TESTS and select 2:T-Test.  For Inpt, choose Stats and press ENTER.  Fill the input screen with the appropriate information.  Choose for the alternative hypothesis and press ENTER.

 

 

Highlight Calculate and press ENTER.

 

 

Or, highlight Draw and press ENTER.

 

 

The P=value is .0559.  So, approximately 5 samples in 100 will result in a sample mean of 18.3 or less, if, in fact, the population mean is equal to 20.  Since the P-value is greater than a, the correct conclusion is to Fail to Reject .