Question

A fast-food chain claims one small order of its tater tots weighs 90 grams. Ava thinks she is getting less than what the restaurant advertises. She weighs the next 14 random orders of tater tots before she eats them and finds the sample mean is 89.3 grams and the standard deviation is 3.71 grams. What conclusion can be drawn at α = 0.05?

There is not sufficient evidence to prove the fast-food chain advertisement is true.

There is sufficient evidence to prove the fast-food chain advertisement is false.

Ava does not have sufficient evidence to reject the fast-food chain's claim.

Ava has sufficient evidence to reject the fast-food chain's claim.

There is not sufficient data to reach any conclusion.

Answer 1

given data are sample n =14

population mean =90 grams

sample mean x =89.3 grams

sample sd s=3.71 grams

null hypothesis H0: - =90

alternative hypothesis Ha:- <90

= level of significance =0.05

test statistic :- t=

t=(89.3-90)/(3.71/)

= -0.7 / 0.9915

= - 0.706

critical region: -

at =0.05 with df=n-1=13 in 1 tail from t table t = -1.771

reject H0 if tcal < -1.771

Decision :-

tcal>t (i.e, -0.706> -1.771)

fail to reject the null hypothesis .

conclusion :-

ava does not have sufficient evidence to reject the fast food chains claim.