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.

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

**a. µ **= 108

**b. **H_{0}: **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.

- Determine the null hypothesis.
- Determine the alternative hypothesis.
- Classify the hypothesis test as two tailed, left tailed, or right tailed.

**a. **H_{0}: **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.

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

**a. **H_{0}: **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.

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

**a. **H_{0}: **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.

- Determine the null hypothesis.
- Determine the alternative hypothesis.
- Classify the hypothesis test as two tailed, left tailed, or right tailed.

**a. **H_{0}: **µ** = 98.2°F

**b.** H_{a}: **µ** ≠ 98.2°F

**c.** The hypothesis test is two tailed.