Stats
Significance
Imagine a study to investigate how different types of mattresses affect premature babies' breathing patterns when they are sleeping. Two mattresses are under consideration a regular mattress and a waterbed. Half the babies will be randomly assigned to sleep on regular mattresses in the first periot and then on waterbeds in the second period. For the remaining babies it will be the reverse [waterbeds in the first period and then on regular mattresses in the second period}. The number of breathing interruptions per hour of sleep for an individual baby is calculated using both the number of times the baby's breathing stopped for more than 21'} seconds and the length of time the baby was asleep. Therefore the question is. does the type of mattress affect premature babies' breathing patterns? In addition. the researchers consider a difference of less than 0.25 interruptions per hour. on average. would be of no consequence. whereas a difference of at least 0.25- interruptions per hour could result in major health issues. Some possible outcomes of the study are: - "m "m Notes: 1. Diff I number of breathing intermptions per hour on a regular mattress number of breathin: interruptions per hour on a waterbed 2. The hypotheses associated with the quoted Pvoiues are: Hg: mg I D vs H1: pg,\" 3% where pm\" is the underlying mean difference in the number o breathing interruptions per hour for premature babies sleeping on a regular mattress and those sleeping on a waterbed. El} What is the hypothesised value? l 5'3\"\" V b] Select the correct options to complete the sentence about Case 4: The estimated difference in Case 4 {x31}, - 411.533 is| IE-E'ECTI V odd} standard errorsl lSEIBl V lthe hypothesised yalue. c] Ilul'il'hich case{s} demonstrates. at the 5% level of significance. that the observed mean difference. XBJH. is statistically different from the hypothesised value? | [Select] VI d] In which caselsl are we are able to claim that the underlying mean difference in the number of breathing interruptions per hour between the two mattress types - has practical signiflca ncel [533\"] V c) Which case(s) demonstrates, at the 5% level of significance, that the observed mean difference, xpiff, is statistically different from the hypothesised value? [ Select ] d) In which case(s) are we are able to claim that the underlying mean difference in the number of breathing interruptions per hour between the two mattress types - has practical significance [ Select ] - does not have practical significance [ Select ] e) Select one case in which we have learned nothing useful about the underlying mean difference in the number of breathing interruptions per hour between the two mattress types [ Select ] f) Suppose the actual outcome for the study is: XDiff se(xDuff) P-value 95% CI Case 6 0.55 0.045 0.0015 10.46, 0.60) Select the correct option to complete the sentences interpreting this output: In this case the difference between the mean difference of 0.52 breathing interruptions per hour and the hypothesised value of zero |[ Select ] V statistically significant (at the 5% level). We [ Select ] able to claim that the underlying mean difference has practical importance. With 95% confidence, on average, the number of breathing interruptions per hour when using the regular mattress are estimated to be somewhere between [ Select ] v and [ Select ] v [ Select ] V than that when using the waterbed. Based on these results I would [ Select ] (Note: This question was based on an imaginary study and should not be used to make real life decisions!)
