Question

The director of a daycare center noticed that the infants were getting more diaper rashes than usual in the summer time. The policy of the center was to change the diapers on a schedule every three hours. The director wanted to find out if adjusting the diaper-changing schedule to every two hours would significantly reduce the number of diaper rashes. Since some of the infants seemed to have more sensitive skin, she decided to directly compare the number of diaper rashes for each individual infant when the diaper was changed every three hours versus every two hours. For the first week, the daycare center changed the diapers as usual every three hours and noted the number of days that each infant had symptoms of a diaper rash. During the second week, the teachers changed diapers every two hours and recorded the number of days with symptoms of a diaper rash. At the end of the two weeks, they compared for each individual infant the number of days with symptoms of a diaper rash when the diapers were changed every three hours versus every two hours.Let μ 1 and μ 2 represent the mean number of days with symptoms of a diaper rash when diapers were changed every three hours and two hours, respectively, and let μ d be the mean of the differences in thenumber of days with symptoms of a diaper rash (diaper rash days when changed every three hours minus diaper rash days when changed every two hours).What is the appropriate null and alternative hypotheses?

Answer 1

Let μ1 and μ2 represent the mean number of days with symptoms of a diaper rash when diapers were changed every three hours and two hours, respectively.

Let μd be the mean of the differences in the number of days with symptoms of a diaper rash.

The null hypothesis and alternative hypotheses are two mutually exclusive things about any population. The null hypothesis is that, which is to be actually tested but an alternative hypothesis gives an alternative to the null hypothesis.

Here the appropriate null and alternative hypotheses will be :

H0: μd=0 (null)

Ha: μd>0 (alternative)

This given study is a matched pair design study, so we are using μd : the mean of the differences.

Also, here we are testing if the number of diaper rashes are more when they are changed every 3 hours than 2 hours. This is why we chose the above hypothesis H0: μd = 0 and Ha: μd > 0.

Answer 2

Let μ1 and μ2 represent the mean number of days with symptoms of a diaper rash when diapers were changed every three hours and two hours, respectively.

Let μd be the mean of the differences in the number of days with symptoms of a diaper rash.

The null hypothesis and alternative hypotheses are two mutually exclusive things about any population. The null hypothesis is that, which is to be actually tested but an alternative hypothesis gives an alternative to the null hypothesis.

Here the appropriate null and alternative hypotheses will be :

H0: μd=0 (null)

Ha: μd>0 (alternative)

This given study is a matched pair design study, so we are using μd : the mean of the differences.

Also, here we are testing if the number of diaper rashes are more when they are changed every 3 hours than 2 hours. This is why we chose the above hypothesis H0: μd = 0 and Ha: μd > 0.