Question

Question 3(Multiple Choice Worth 2 points) (07.01 MC) 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 o tater tots before she eats them and finds the sample mean is 89.3 grams and the standard deviation s 37 gams. What con us can be drawn at a There is not sufficient evidence to prove the fast-food chain advertisement is true. O 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. OAva has sufficient evidence to reject the fast-food chain's claim OThere is not sufficient data to reach any conclusion.

Answer 1

Solution :

Question (3) :

It is given that a fast-food chain claims one small order of its tater tots weighs 90 grams. Ava thinks that she is getting less than what the restaurant advertises. She weighs the next 14 random order of tater tots before she eats them and finds the sample mean is 89.3 grams and the standard deviation is 3.71 grams.
We have to find the conclusion at =0.05.

We have to conduct a t - test to test the claim about the population mean, at a given level of significance using the sample statistics. We consider that the population is normally distributed.

To determine the appropriate null and alternative hypothesis :

Ho : μ-90 US Ha : μ<90 : μ Population Mean

where,   is the population mean weight of the tater tots of the fast-food chain.

To calculate the standardized test statistic :

Thus , The appropriate test statistic is given as ,

,40 ~ Ņ(0, 1) [under Hol


where, n= Sample Size ; -= Sample Mean-一〉 '.xi


7L Ho-Specified value of μ : s-Sample SD- X(xi-x)2

From the data given , we have the following information :

Thus , the value of the test statistic is given as ,To find the p - value of the test :

The p - value of the t-test is given as ,

To conclude from the test hypothesis test using alpha = 0.06 level of significance :

Conclusion : The p - value is greater than the level of significance , so there is no sufficient evidence to conclude that the population mean weight is not 90 grams (Do not Reject H₀)

Correct Option (C) Ava does not have sufficient evidence to reject the fast-food chain's claim...................(Ans)

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Question (4) :

It is given that a research company wants to determine whether there is a huge difference in effectiveness of a brand-name Ibuprofen and generic Ibuprofen.
We have to find the appropriate hypothesis for this testing scenario.

Let  $mu_1$ equal the mean of the effectiveness of brand-name Ibuprofen generic Ibuprofen.
Let   equal the mean of the effectiveness of brand-name of generic Ibuprofen.

The Appropriate Hypothesis for this testing scenario is given below :

Thus, the Correct Option is Option (C) ...................................... (Ans)

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