PLEASE ANSWER NUMBER 3 1) A cereal company is marketing a product that claims it

Question

PLEASE ANSWER NUMBER 3

1) A cereal company is marketing a product that claims it contains only 100 calories. You want to test the hypothesis that in fact their product on average does has 100 calories.

(a) What type of significance test would you perform? SINGLE SAMPLE T TEST

2) You go out a sample 7 packages of the product and find that the mean of your sample X---bar is 101 and the standard deviation of you sample ‘s’ is 1.

(a) Perform the significance test… what is the probability that the null hypothesis is true? DF= 6, p-VALUE 0.0382

(b) At an alpha level of 0.05, would you accept or reject the null hypothesis? REJECT

3) The company switches to a new a new form of sweetener and you want to know if this change corresponds to there being a different amount of calories in the product. So you go out and collect 7 of the new formulation of the product and determine that the sample mean of these new packages is 103 calories with a standard deviation ‘s’ of 2.

a) What type of significance test would you perform between the data collected here with those collected in ‘2’ ?

b) Perform the test… what is the probability that the null hypothesis is true?

c) At an alpha level of 0.05, would you accept or reject the null hypothesis?

Explanation / Answer

a)
t-test for assessing the significance of difference between the sample mean and population mean:

b) x = 101 , mean = 103 , n = 7 , s = 2

t = ( x - mean) / ( s /sqrt(n))
= ( 101 - 103) / ( 2 / sqrt(7))
= -2.645

c) P value is calculated using t = -2.645 , df = 6
p value = .0382
we reject the null hypothesis

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