Question

Write the null and alternative hypotheses for each situation described below, and indicate whether each test would be left-tailed, right-tailed, or two-tailed. Make sure that you use the correct population parameter. To submit the assignment, you may just type your answers in the text box. (You don't have to worry about typing subscripts or Greek letters on this assignment unless you want to. For example, for , you could type H0: mu = 30.)

1. A cereal manufacturer claims that, for a particular brand of cereal, the average amount of cereal in a box is 20 ounces. A consumer advocate believes that the boxes are underfilled.

2. In the past, it was reported that 30% of American adults were obese. A health researcher believes that the proportion is now different from that.

3. A homeowner claims that the average monthly water bill is $80.00. A potential buyer believes that the average bill is higher than that.

Answer 1

1.

Parameter : Population mean : : the average amount of cereal in a box . A consumer advocate believes that the boxes are under filled i.e < 20 (This goes into the alternative hypothesis ; and left tailed as we have < in the alternative hypothesis)

Null hypothesis : Ho : = 20 ounces

Alternative Hypothesis : H1 : < 20 ounces

Left Tailed test

2.

Parameter : Population Proportion : p : Proportion of American adults were obese :  30/100 = 0.30

A health researcher believes that the proportion is now different from that. (p 0.30; This goes into the alternative hypothesis ; and two tailed as we have   in the alternative hypothesis)

Null hypothesis : Ho : p = 0.30

Alternative Hypothesis : H1 : p 0.30

Two Tailed test

3.

Parameter : Population mean : :average monthly water bill : $80.00; A potential buyer believes that the average bill is higher than that.(i.e >$80.00 (This goes into the alternative hypothesis ; and right tailed as we have > in the alternative hypothesis)

Null hypothesis : Ho : = $80.00

Alternative Hypothesis : H1 : > $80.00

Right Tailed test

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The null and alternative hypotheses are two mutually exclusive statements about a population. A hypothesis test uses sample data to determine whether to reject the null hypothesis.

Null hypothesis (H0)

The null hypothesis states that a population parameter (such as the mean, the standard deviation, and so on) is equal to a hypothesized value. The null hypothesis is often an initial claim that is based on previous analyses or specialized knowledge.

Alternative Hypothesis (H1)

The alternative hypothesis states that a population parameter is smaller, greater, or different than the hypothesized value in the null hypothesis. The alternative hypothesis is what you might believe to be true or hope to prove true.

One-sided and two-sided hypotheses

The alternative hypothesis can be either one-sided or two sided.

Two-sided

Use a two-sided alternative hypothesis (also known as a non-directional hypothesis) to determine whether the population parameter is either greater than or less than the hypothesized value. A two-sided test can detect when the population parameter differs in either direction, but has less power than a one-sided test.

One-sided

Use a one-sided alternative hypothesis (also known as a directional hypothesis) to determine whether the population parameter differs from the hypothesized value in a specific direction. You can specify the direction to be either greater than or less than the hypothesized value. A one-sided test has greater power than a two-sided test, but it cannot detect whether the population parameter differs in the opposite direction.