Question

Hypothesis Test in the News

School programmes encouraging children to take more exercise and eat healthily are unlikely to have any real effect on childhood obesity, a study in the British Medical Journal suggests.

More than 600 primary school pupils in the West Midlands took part in a 12-month anti-obesity programme. But the study found no improvements in the children's diet or activity levels.

Public health officials said they were working with industry to make food healthier.They also said a sugar reduction programme and the government's sugar tax would help to tackle childhood obesity.

The researchers, from the University of Birmingham, said families, communities and the food industry probably had more of an influence than school initiatives.

In the UK, one in four children starts school overweight and one in 10 is obese. By the end of primary school, the percentage of obese children has doubled to one in five. The programme introduced in schools in the study included:

a daily opportunity to do 30 minutes of additional exercise

a six-week healthy eating and exercise programme in conjunction with Aston Villa Football Club

healthy cooking workshops once a term for families

highlighting of local family physical activities

The researchers set up the healthy lifestyle programme for six and seven-year-olds in 26 primary schools. They then compared the results with more than 700 children in another 28 primary schools who did not take part.

When the researchers followed up the children 15 months and 30 months after it started, they found no statistically significant reductions in BMI (body mass index) and no improvements in energy expenditure, body fat measurements or activity levels - compared with those not taking part.

1. Let mu programme denote the average reduction in BMI for children in the program. Let mu no programme denote the average reduction in BMI for children not in the program. What are the appropriate hypotheses for testing that the reduction in BMI was greater for students in the programme?

2. Based on the article were the results statistically significant?

3. Assume that the hypothesis test was performed at the 5% significance level what was the conclusion of the hypothesis test?

Answer 1

(1) here the null and alternate hypothesis would be like this

null hypothesis H0:_program=_{not in program}

alternate hypothsis Ha::_program>_{not in program} ( right tailed directional )

(2) statistically not significant ( or insignificant)

here the accepted null hypothesis, as they found no statistically significant reductions in BMI (body mass index) and no improvements in energy expenditure, body fat measurements or activity levels - compared with those not taking part.

(3) at the 5% significance level , we can conlude that  there is no improvements in the children's diet or activity levels.