Question

A manufacturer of hard safety hats for construction workers is concerned about the mean and the variation of the forces helmets transmit to wearers when subjected to a standard external force. The manufacturer desires the mean force transmitted by helmets to be 800 pounds (or less), well under the legal 1,000-pound limit, and σ to be less than 40. A random sample of n = 45 helmets was tested, and the sample mean and variance were found to be equal to 835 pounds and 2,340 pounds2, respectively.

(a) If μ = 800 and σ = 46, is it likely that any helmet, subjected to the standard external force, will transmit a force to a wearer in excess of 1,000 pounds? Explain. (Use α = 0.05.)

(b) Do the data provide sufficient evidence to indicate that when the helmets are subjected to the standard external force, the mean force transmitted by the helmets exceeds 800 pounds? (Use α = 0.05.)

State the null and alternative hypotheses.

State the test statistic. (Round your answer to three decimal places.)

State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)

State the conclusion.

Answer 1

Here we have P) z.7 4-33) ー,-0-399993 10-00000 Since obtained pro ba b Standard ex*er na 48.3 H: 시,2800 Ha : 시 800 χ -4-835-800 4 &.37 α'-0.05 and dfニ45-1244- AST AT 〉 1。68 l-68

v Pounds