Question

The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box, with ?? = 9. A random sample of 94 Nero matchboxes shows the average number of matched per box to be 43.1. Using a 5% level of significance, can you say that the average number of matches per box is more than 40?

a) what is the level of significance? state the null and alternate hypothesis

b) what sampling distribution will you use? what assumptions are you making? compute the sample test statistic and corresponding distribution value?

c) find the p value. sketch the sampling distribution and show the area corresponding to the p value?

d) will you reject or fail to reject the null hypothesis

e)interpret your conclusion in the context of the application

Answer 1

a)
H0 : mu = 40
Ha: mu > 40

b)

z sampling distribution

Assumptions:

The sample must be reasonably random.

The data must be from a normal distribution or large sample (need to check n ≥ 30 ).

σ must be known.

The sample must be less than 10% of the population so that
sigma/sqrt(n) is valid for the standard deviation of the sampling distribution of xbar .

test statistics:

z = (xbar -mu)/(sigma/sqrt(n))
= ( 43.1 - 40)/(9/sqrt(94))
= 3.34

c)

p value = 1 - P(z<3.34)

P value = 0.0004

d)

Reject H0 as p value < 0.05

e)

There is suficient evidence to support the clai that the average number of matches per box is more than 40