Question

The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 56 gm. The process standard deviation is known to be 0.77 gm. A random sample of 49 candy bars yields a mean weight of 55.82 gm.

(a) State the hypotheses to test whether the mean is smaller than it is supposed to be.
(b) What is the test statistic?
(c) At α = .05, what is the critical value for this test?
(d) What is your conclusion?

Answer 1

|z(s)| < |z(c)|

Then z(s) is in the acceptance region we accept H₀.

We don´t have evidence to support that candy bar mean weight is below 56 gm

Explanation:

Goal mean μ = 56 gm

standard deviation σ = 0,77

From random sample:

mean x = 55,82

sample size n = 49

We assume a normal distribution ( is a manufacturing controlled process)

a) Hypothesis Test:

Null Hypothesis H₀ x = μ

Alternative Hypothesis Hₐ x < μ

Alternative hypothesis is telling us that the test is a one-tail test to the left

as n > 30 we use the normal distribution.

b) z(s) = ( x - μ ) / σ / √n

z(s) = 55.82 - 56 ) * 7 / 0,77

z(s) = 0,18*7/0,77

z(s) = - 1.6363

c) if significance level is α = 0.05 then α/2 = 0,025

Then from z table, z score for 0,025 z(c) = -1.96

d) Comparing z(c) and z(s) modules

|z(s)| < |z(c)|

Then z(s) is in the acceptance region we accept H₀.

We don´t have evidence to support that candy bar mean weight is below 56 gm