A recent study of food portion sizes reported that over a 17-year period, the av

Question

A recent study of food portion sizes reported that over a 17-year period, the average size of a soft drink consumed by Americans aged 2 years and older increased from 13.1 ounces (oz) to 19.9 oz. The authors state that the difference is statistically significant with P < 0.01.† Explain what additional information you would need to compute a confidence interval for the increase, and outline the procedure that you would use for the computations. (Select all that apply.)

a) Sample sizes and a more accurate P-value could be used to find the confidence interval. In this case we could determine standard deviations and the confidence interval in the usual way.

b) t and degrees of freedom could be used to find the confidence interval. In this case we could compute SED and use degrees of freedom to find t*.

c) Degrees of freedom and a more accurate P-value could be used to find the confidence interval. In this case we could determine t, then calculate SED and t*.

d) Standard deviations and degrees of freedom could be used to find the confidence interval. In this case we could now find the P-value, which could be used to find SED.

e) Sample sizes and standard deviations could be used to find the confidence interval. In this case we could find the interval in the usual way.

I have tried the possible combinations below and they are the WRONG ANSWER.

b&d, b, d, d&e, a&d

Explanation / Answer

Answer is (b) , (c) and (e)

(b) t = mean difference/ SED

if t is given , we can find SED

And use degrees of freedom to find critical value of t ( t*)

Confidence interval is mean difference+/- t* SED

(c) if degrees of freedom and more accurate p value given , we can find t

From t we can find SED , from degrees of freedom we can find t*

(e) if sample size and standard deviation given we can compute SED

SED= sd/ sqrt(sample size)

Degrees of freedom = sample size-1 and then we can find t*

Then we can compute confidence interval

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