Question

The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box, with σ = 11. A random sample of 95 matchboxes shows the average number of matches per box to be 43.0. Using a 1% level of significance, can you say that the average number of matches per box is more than 40?

What are we testing in this problem?

single meansingle proportion    

(a) What is the level of significance?


State the null and alternate hypotheses.

a.H₀: p = 40; H₁: p ≠ 40

b.H₀: p = 40; H₁: p > 40    

c.H₀: p = 40; H₁: p < 40

d.H₀: μ = 40; H₁: μ ≠ 40

e.H₀: μ = 40; H₁: μ > 40

f.H₀: μ = 40; H₁: μ < 40

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t, since we assume that x has a normal distribution with unknown σ.The standard normal, since we assume that x has a normal distribution with unknown σ.    The standard normal, since we assume that x has a normal distribution with known σ.The Student's t, since we assume that x has a normal distribution with known σ.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

_______
(c) Find the P-value. (Round your answer to four decimal places.)

______

Answer 1

The statistical software output for this problem is :

(a)

level of significance = 0.01

E)

H₀: μ = 40; H₁: μ > 40

  The standard normal, since we assume that x has a normal distribution with known σ .

Test statistics = 2.66

P-value = 0.0039