Question

A sample of 27 blue jellybeans with a mean weight of 0.8590 g was taken. Assume that σ  is known to be 0.0565 g. Consider a hypothesis test that uses a 0.05 significance level to test the claim that the mean weight of all jellybeans is equal to 0.8570 g (the weight necessary so that bags of jellybeans have the weight printed on the package). Assume the weight of jellybeans is normally distributed.

a. What are the null and alternative hypotheses?

b. What is the value of the test statistic? (Round to two decimal places as needed.)

c. What is the P-value? (Round to four decimal places as needed.)

d. What is the conclusion about the null hypothesis (reject, fail to reject)?

Answer 1

a)

H0: = 0.8570

Ha: 0.8570

b)

Test statistics

z = ( - ) / ( / sqrt(n) )

= ( 0.8590 - 0.8570) / ( 0.0565 / sqrt(27))

= -0.18

c)

p-value = 2 * P(Z < z)

= 2 * P(Z < -0.18)

= 2 * 0.4286

= 0.8572

d)

Since p-value > 0.05 level, fail to reject null hypothesis