NOTE: Use the calculator, however, show what you plugged please. A bag of Dorito
ID: 3296262 • Letter: N
Question
NOTE:
Use the calculator, however, show what you plugged please.
A bag of Doritos is marked with a net mean weight of 28.3 grams. A group of students sample 36 bags and find a mean of 28.48 grams and a standard deviation of 0.36 grams. The students would like to test if the mean weight is different from the claimed weight on the Dorito's bag. Let alpha = 0.05. (a) State appropriate hypothesis (b) Check conditions (c) Calculate the test statistic. What distribution it follows under the null hypothesis? (d) Find the rejection region (e) Compute the p-value (f) State your conclusion based on you rejection region or p-value. (g) If the actual mean weight is 28.3 grams, did you make a correct conclusion or which type of error did you make?Explanation / Answer
a) The hypothesis is
H0 : The mean is not different from the claimed weight on the Dorito bag
H1 : The mean is statistically different from the claimed weight on the Dorito bag
The values are
Pop mean = 28.3 , sample mean = 28.48 , SD = 0.36
N = 36 , as N> 30 , we use a t test as the popularion standard deviation is not known
t = X1-X2/SE = (28.3-28.48)/(0.36/sqrt(36))
hence the Z = -3 , now we calculate the degree of freedom as = n-1 = 36-1 = 35
looking at the t table we see that the critical value is +-2.03
as the Tcritical <t calc hence we reject the null hypothesis
Again , using the t table we see that the p value is 0.0049 (approx). Hence we reject null hypothesis and conclude that The mean is statistically different from the claimed weight on the Dorito bag
as the claim is 28.3 grams and we conclude that it is different from 28.3 grams , so we make an error in the last question. We rejected the null hypothesis when we should not. Hence we made a type 2 error
remember ]
type 1 : accepting null hypothesis when we should not
type 2 :rejecting null hypothesis when we should not
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