Question

The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box, with σ = 8. A random sample of 94 matchboxes shows the average number of matches per box to be 42.2. 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 mean single proportion (a) What is the level of significance? State the null and alternate hypotheses Ho: μ-40; H1: μ > 40 O Ho: p 40; H1: p> 40 Ho: p = 40, H1: p # 40 ○ Ho: p = 40, H1: pく40 (b) What sampling distribution will you use? What assumptions are you making? 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 unknown 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 (or estimate) the P-value O P-value0.250 o 0.125 <p-value 0 0.050くP-value O 0.025 <p-value ( 0.005 <p-value O p-value< 0.005 0.250 0.125 0.050 0.025

Answer 1

Option-A) single mean

a) Level of signficance= 0.01

Option-A) H₀: µ = 40, H₁ : µ > 40

b) Option-B) The standard normal , since we assume that z has a normal distribution with known sigma

Test statistic

                     $=\frac{42.2-40}{8/\sqrt{94}}$

                     = 2.67

c) P-value = P(Z > 2.67) = 1 - P(Z < 2.67) = 1 - 0.9962 = 0.0038

Option-F) P-value < 0.005