Claim: The mean weight of beauty pageant winners is 108 pounds. A study of 16 randomly selected beauty pageants resulted in a mean winner weight of 113 pounds.

1. Express the original claim in symbolic form.
2. Identify the null and the alternative hypotheses.

a. µ = 108

b. H₀: µ = 108

H_a: µ ≠ 108

Cadmium, a heavy​ metal, is toxic to animals.​ Mushrooms, however, are able to absorb and accumulate cadmium at high concentrations. Some governments have a safety limit for cadmium in dry vegetables at 2.5 parts per million​ (ppm). A hypothesis test is to be performed to decide whether the mean cadmium level in a certain mushroom is less than the​ government's recommended limit.

1. Determine the null hypothesis.
2. Determine the alternative hypothesis.
3. Classify the hypothesis test as two​ tailed, left​ tailed, or right tailed.

a. H₀: µ = 2.5 ppm

b. H_a: µ < 2.5 ppm

c. The hypothesis test is left tailed.

The mean local monthly bill for cell phone users in this country was ​$44.41 in 2001. A hypothesis test is to be performed to determine whether last​ year's mean local monthly bill for cell phone users has increased from the 2001 mean of ​$44.41.

1. Determine the null and alternative hypotheses.​
2. Classify the hypothesis test as two​ tailed, left​ tailed, or right tailed.

a. H₀: µ = $44.41

H_a: µ > $44.41

b. Right tailed

The mean length of imprisonment for​ motor-vehicle theft offenders in this country is 14.1 months. A hypothesis test is to be performed to determine whether the mean length of imprisonment for​ motor-vehicle theft offenders in this city differs from the national mean of 14.1 months.

1. Determine the null and alternative hypotheses.​
2. Classify the hypothesis test as two​ tailed, left​ tailed, or right tailed.

a. H₀: µ = 14.1 months

H_a: µ ≠ 14.1 months

b. Two-tailed

A study by researchers at a university addressed the question of whether the mean body temperature of an animal is 98.2°F. Among other​ data, the researchers obtained the body temperatures of 109 healthy animals. Suppose you want to use those data to decide whether the mean body temperature of healthy animals differs from 98.2°F.

1. Determine the null hypothesis.
2. Determine the alternative hypothesis.
3. Classify the hypothesis test as two​ tailed, left​ tailed, or right tailed.

a. H₀: µ = 98.2°F

b. H_a: µ ≠ 98.2°F

c. The hypothesis test is two tailed.