1 The occupational safety and health commission is concerned with asbestos exposure in the workplace. A building is only considered to be safe if its mean asbestos exposure is 0.10 fibers per cubic centimetre (f/cm^3) or less. Exposure levels in the building are known to follow a normal distribution with standard deviation 0.03 f/cm^3. A hypothesis test is conducted at the 5% level of significance to determine whether the building is unsafe.

What are the null and alternative hypotheses?

a H0: = 0.10 vs Ha: 0.10

b H0: x = 0.10 vs Ha: x > 0.10

c H0: x = 0.10 vs Ha: x < 0.10

d H0: = 0.10 vs Ha: > 0.10

e H0: = 0.10 vs Ha: < 0.10

2 Asbestos exposure levels are measured at twelve randomly selected locations in one building. The sample mean is calculated to be 0.11 f/cm3. What is the value of the test statistic for the appropriate test of significance?

keep 4 decimal places in intermediate calculations and report your final answer to 2 decimal places.

answer:

3 Packages of frozen peas are supposed to have a mean of 10 oz. The manufacturer wishes to detect if the mean is either too low (which is illegal) or too high (which reduces profits). It is known that weights follow a normal distribution with standard deviation 0.25 oz. The mean weight of a random sample of 30 bags is found to be 9.9 oz.

what is the P-value of the appropriate test of significance?

keep 4 decimal places in intermediate calculations and report your final answer to 4 decimal places.

answer:

4 The prosecutor in a criminal trial introduces a key piece of evidence -- a letter written by the criminal that was left at the scene of the crime. The defendant in the case is left handed, and handwriting experts can often distinguish between the writing of left handed and right handed people. The prosecutor asks an expert to analyze the letter. The expert tests the hypotheses

H0: the writer of the letter is right handed.

Ha: the writer of the letter is left handed

the handwriting expert determines a P- value of 0.002. Using a 1% level of significance, we conclude that:

a the probability that the letter was written by a right handed person is 0.002

b there is sufficient evidence that the letter was written by a left handed person

c the probability that the letter was written by a left handed person is 0.002

d there is insufficient evidence that the letter was written by a left handed person.

e there is sufficient evidence that the letter was written by a right handed person.