Course Notes - Department of Mathematics and Statistics

ALTERNATIVE HYPOTHESESTwo types:Study based - implies we do not know at the beginning of the studyabout the effect of a new treatment. Leads to a two sided test(two parameter values are not equal to each other).Data based - suggested by the collected data (usually suggests treatmentbenefit). Leads to a one sided test (one parameter value isgreater than or less than the other).TESTING STEPS1. Set up the null hypothesis (H 0 ) about the population parameter ofinterest e.g. parameter = current (null) value.2. Propose the alternative hypothesis (H A ) e.g. parameter ≠ currentvalue.3. Calculate the test statistic.4. Calculate the p-value (probability of observing the test statisticfrom 3).The Test StatisticThis is the standardised value of the sample parameter i.e. a z-scoreor t-score:observed sample value - null valueTest statistic =estimated standard errori.e. the number of standard deviations from the null value to thesample value.The p-value• This is the probability of observing the value of the test statistic,or a value more extreme, calculated under the assumption thatH 0 is true.• We draw appropriate conclusions if the pvalue is less than 0.05 -if the p-value is less than 0.05 we have significance at the 5% leveland if less than 0.01 we have significance at the 1% level.120