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 ? 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 850 pounds and 2,380 pounds², respectively.

(a) If ? = 800 and ? = 40, 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 ? = 0.05.)

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(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 ? = 0.05.)

State the null and alternative hypotheses.

H₀: ? > 800 versus H_a: ? = 800H₀: ? = 800 versus H_a: ? < 800    H₀: ? = 800 versus H_a: ? > 800H₀: ? > 800 versus H_a: ? < 800H₀: ? = 800 versus H_a: ? ? 800

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

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

t >

t <

State the conclusion.

H₀ is not rejected. There is sufficient evidence to indicate that the mean force transmitted by the helmets exceeds 800 pounds.H₀ is rejected. There is sufficient evidence to indicate that the mean force transmitted by the helmets exceeds 800 pounds.    H₀ is not rejected. There is insufficient evidence to indicate that the mean force transmitted by the helmets exceeds 800 pounds.H₀ is rejected. There is insufficient evidence to indicate that the mean force transmitted by the helmets exceeds 800 pounds

Answer 1

Solution B:

given the mean force transmitted by the helmets exceeds 800 pounds

H0:m=800

H1:mu>800

alpha=0.05

? = 800 versus Ha: ? > 800

State the test statistic.

t=sample mean-[population mean/samplesd/sqrt(sample size)

sample sd=sqrt(variance)=sqrt(2380 )=48.78524

t=850-800/48.78524/sqrt(45)

t=6.875

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

t=6.875

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

its one tail test

right tail.

use excel

=T.INV(0.05;44)

-1.680229977 T>1.680

CONCLUSIN:

T>T CRIT

6.875>1.680

REJECT HO

H0 is rejected. There is sufficient evidence to indicate that the mean force transmitted by the helmets exceeds 800 pounds.