Question

HW8

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

(a) state your Null and Alternative hypotheses?

2) You go out a sample 10 packages of the product and find that the mean of your sample X---bar is 102 and the standard deviation of you sample ‘s’ is 1.

(a) Perform the appropriate significance test… what is the probability that the null hypothesis is true?

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

3) The company switches to 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 10 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 3. Recall: the data you collected for the original formulation had a mean of 102 and s = 1;

a) What type of significance test would you perform between the data collected here with those collected in ‘1’ ?

b) Should the test be 1 tailed or two tailed?

c) Perform the test, what is the probability the null hypothesis is true?

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

HW9

1) The company comes out with yet another sweetener and you want to know if any of these changes has changed amount of calories in the product. So you go out and collect 10 of the new packages of the product and determine that the sample mean of these is 99 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’ and ‘3’ for the HW8 problem above (i.e. you now have three groups)?

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?

please show work thank you:)

Answer 1

1.)