Is this null hypothesis wrong?

[Tyto alba]

'In inferential statistics, the term "null hypothesis" is a general statement or default position that there is no relationship between two measured phenomena, or no association among groups.' (wiki)

The book I'm following has to say :

Q: In a nutritional study 13 students were given a usual diet with vitamin tablets and 12 set of other students were given only the normal diet. After 12 months their weights are measured as given below (a 2 x 13 table in which weight gains of the two set of students are mentioned) Can you say that vitamins were responsible for this difference?

A: Ho= Vitamins are responsible for this difference HA= just the ooposite, not responsible

The t-value turned out to be more the p-value and they rejected the Ho

P.S. I'm sure it isn't right because Vitamin rich diet does cause weight gain and given the concept of null hypothesis the Ho assumed in the excerpt should be wrong.

 

[Stephen Tashi]

Q: In a nutritional study 13 students were given a usual diet with vitamin tablets and 12 set of other students were given only the normal diet. After 12 months their weights are measured as given below (a 2 x 13 table in which weight gains of the two set of students are mentioned)

Did you state this problem correctly? A 2x13 table has 26 entries, but you only mentioned 13+12 = 25 students.

 

[MarneMath]

The book's null hypothesis is rather wrong. You should flip the null hypothesis and alternative hypothesis statements. The default position for your null hypothesis should be that there is no effect observed.

 

[mjc123]

Can you say that vitamins were responsible for this difference?

The question is poorly expressed. Your null hypothesis should be that there is no (statistically significant) difference between the vitamin group and the non-vitamin group. If there is a difference (H0 rejected), it is a further conceptual step to say that the vitamins are "responsible" for it. Statistical correlation does not imply causal dependency.