Question

Results from the National Health Interview Survey show that among the U.S. adult population, 45.9% do not meet physical activity guidelines, 3.5% meet only strength activity, 29.0% meet only aerobic activity, and 21.6% meet both strength and aerobic activity. We sampled 4475 adults from Ohio and the results were as follows: 50.0% do not meet physical activity guidelines, 5.0% meet only strength activity, 35.0% meet only aerobic activity, and 10.0% meet both strength and aerobic activity. Conduct an appropriate hypothesis test to determine if the distribution in physical activity among Ohioans is similar to the U.S. population. Interpret your results.

Answer 1

Solution:

   We are given that: Results from the National Health Interview Survey show that among the U.S. adult population,

45.9% do not meet physical activity guidelines,

3.5% meet only strength activity,

29.0% meet only aerobic activity, and

21.6% meet both strength and aerobic activity.

These are the expected percentage values.

Sample of 4475 adults from Ohio is taken and the results were as follows:

50.0% do not meet physical activity guidelines,

5.0% meet only strength activity,

35.0% meet only aerobic activity, and

10.0% meet both strength and aerobic activity.

These are the observed percentage value.

We have to conduct an appropriate hypothesis test to determine if the distribution in physical activity among Ohioans is similar to the U.S. population.

Thus we use following steps:

Step 1) State H0 and H1:

H0: The distribution in physical activity among Ohioans is similar to the U.S. population.

Vs

H1: The distribution in physical activity among Ohioans is not similar to the U.S. population.

Step 2) Find test statistic value:

Since we have to test if observed percentage of given sample is similar to expected percentage, we use Chi-square test of goodness of fit.

Thus Chi-square test statistic formula is:

Where Oi = Observed frequencies and Ei = Expected frequencies

N = total sample size.

Thus we need to find Observed frequencies and expected frequencies from given percentage values.

we mulitply each percent value by 4475.

	Obs Percentage	Obs Freq Oi	Exp Percentage	Exp Freq Ei	Oi^2/Ei
do not meet physical activity guidelines	50%	2237.5	45.90%	2054.025	2437.364
meet only strength activity	5.00%	223.75	3.50%	156.625	319.6429
meet only aerobic activity	35.00%	1566.25	29%	1297.75	1890.302
meet both strength and aerobic activity	10.00%	447.5	21.60%	966.6	207.1759
		4475

Thus Chi-square test statistic:

Step 3) Find Chi-square critical value:

df = k - 1 = 4 - 1 = 3

Level of significance = 0.05

Chi-square critical value = 7.815

Step 4) Rejectiom region:

Reject H0 if Chi-square test statistic value > Chi-square critical value, otherwise we fail to reject H0.

Since Chi-square test statistic value = 379.484 > Chi-square critical value = 7.815 , we reject H0.

Step 5) Conclusion:

Since we have rejected null hypothesis , we conclude that: the distribution in physical activity among Ohioans is different from the U.S. population.