A sample of 27 blue jellybeans with a mean weight of 0.8550g was taken. assume t

Question

A sample of 27 blue jellybeans with a mean weight of 0.8550g was taken. assume the weight of jellybeans is normally distributed and that standard deviation is known to be 0.0565g. use a 0.05 significance level to test the claim that the mean weight of all the jellybeans is equal to 0.8515 (the weight necessary so that the bags of jellybeans have the weight printed on the package). identify the null and alternative hypothesis, test statistic, p-value, and state the final conclusion that addresses the original claim.

Explanation / Answer

Given mean = 0.8550 , SD = 0.0565 n = 27

The hypothesis formulation is as follows :

H0 : the mean weight of all the jellybeans is not equal to 0.8515

H1 : the mean weight of all the jellybeans is equal to 0.8515

The t test is

x-mu/(sd/sqrt(n)) , putting the values we get

(0.8550-0.8515)/(0.0565/sqrt(27)) =

0.3218

now t critcal value for df = 27-1 = 26 and alpha = 0.05 is

2.055

as the t stat < t critical we fail to reject the null hypothesis and conclude that the mean weight of all the jellybeans is not equal to 0.8515

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