Question

Sally measures the amount of CO₂ in a pint soda bottle by weight loss; she shakes the bottle vigorously and then slowly opens the cap, letting the gas escape. Three measurements on Brand X indicate a loss of 2.2 ± 0.2 g of gas, while three measurements on Brand Y shows a loss 2.4 ± 0.3 g. (The ± indicates standard error.) Do Brands X and Y have different amount of CO₂?

Answer 1

Here we are provided with the means(2.2 and 2.4 respectively) and the standard errors(0.2 and 0.3 respectively) of the measurements of CO2 in two types of pint soda bottle(viz, A and B). Now the amount of CO2 in a pint soda bottle is measured by weight loss after shaking them vigorously.

We are to test wheather the two brands A abd B have different amount of CO2 or not?

Thus the null hypothesis is stated as Ho: vs the alternative H1:

Where denotes the poppulation mean of the co2 in soda A and soda B respectively.

The test statistics is given as: T= and its sample analogy is:T*= ,as are known to us, denotes the square of the standard errors of .

T* follows a satndard normal distribution, and we are to reject the null hypothesis if |T*_observed|> z_0.025

where z_0.025=1.96 and |T*_observed| = 0.5547, thus we accept the null hypothesis at 0.05 level of significance and coonclude that the two brands A abd B have same amount of CO2 in it.