The Nero Match Company sells matchboxes that are supposed tohave an average of 40 matches per box, with σ = 8. Arandom sample of 98 matchboxes shows the average number of matchesper box to be 42.4. Using a 1% level of significance, can you saythat the average number of matches per box is more than 40?

What are we testing in this problem?

single mean single proportion    

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: p = 40; H₁:p < 40H₀: μ = 40;H₁: μ ≠40    H₀: p = 40;H₁: p ≠ 40H₀:μ = 40; H₁: μ <40H₀: p = 40; H₁:p > 40H₀: μ = 40;H₁: μ > 40

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

The Student's t, since we assume that x has anormal distribution with known σ.The standard normal,since we assume that x has a normal distribution withunknown σ.    The Student'st, since we assume that x has a normaldistribution with unknown σ.The standard normal, since weassume that x has a normal distribution with knownσ.

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


(c) Find (or estimate) the P-value.

P-value > 0.2500.125 < P-value <0.250    0.050 < P-value <0.1250.025 < P-value < 0.0500.005 <P-value < 0.025P-value < 0.005

Sketch the sampling distribution and show the area corresponding tothe P-value.

(d) Based on your answers in parts (a) to (c), will you reject orfail to reject the null hypothesis? Are the data statisticallysignificant at level α?

At the α = 0.01 level, we reject the null hypothesisand conclude the data are statistically significant.At theα = 0.01 level, we reject the null hypothesis and concludethe data are not statisticallysignificant.    At the α = 0.01 level,we fail to reject the null hypothesis and conclude the data arestatistically significant.At the α = 0.01 level, we failto reject the null hypothesis and conclude the data are notstatistically significant.

(e) Interpret your conclusion in the context of theapplication.

There is sufficient evidence at the 0.01 level to conclude thatthe average number of matches per box is now greater than 40.Thereis insufficient evidence at the 0.01 level to conclude that theaverage number of matches per box is now greater than40.