Question

For each example below, state the null and alternative hypotheses.1. A light bulb manufacture claims that the mean life of a certain light bulb is 750 hours. The three you purchased only lasted 700 hours.2. As stated by a company’s shipping department, the number of shipping errors per million shipments is 15. Last month, there were 20 errors per million shipments.3. The mean price of a certain model of car is $30,000, according to commercials. However, you stop by five different dealerships, and each has the car listed for more than $30,000.4. A research organization reports that 33% of the residents in Ann Arbor, Michigan are college students. It seems “everyone” who lives there attends the University of Michigan though.5. The results of a recent study show that the proportion of drivers in the United States who wear seat belts when driving is 84%. This number seems “off” to you, and you think it might be a different proportion.

Answer 1

Note that

H₀ = Null hyothesis

Hₐ = Alternative hypothesis

1) H₀: μ = 750

Hₐ: μ < 750

2) H₀: μ = 15

Hₐ: μ > 15

3) H₀: μ = 30,000

Hₐ: μ > 750

4) H₀: p = 0.33

Hₐ: p > 0.33

5) H₀: p = 0.84

Hₐ: p ≠ 0.84

Check Explanation for more detailed form.

Step-by-step explanation

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

In hypothesis testing, especially one comparing two sets of data, the null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test. It usually maintains that, with random chance responsible for the outcome or results of any experimental study/hypothesis testing, its statement is true. It represents a skeptical perspective and is often a claim of no change or no difference.

The alternative hypothesis usually confirms the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test. It usually maintains that significant factors other than random chance, affect the outcome or results of the experimental study/hypothesis testing and result in its own statement. It is the claim researchers hope to prove or find evidence for, and it often asserts that there has been a change or an effect.

For these questions,

Question 1

Null hypothesis will be that the lifetime of any bulb bought will not be significantly different from 750 hours. In mathematical terms,

μ = 750

Alternative hypothesis will be that the lifetimes of the bulbs bought are significantly lesser than 750 hours. In mathematical terms,

μ < 750

Question 2

Null hypothesis will be that the number of shipping errors per million shipments will not be significantly different from 15. In mathematical terms,

μ = 15

Alternative hypothesis will be that the number of shipping errors per million shipments is significantly greater than 15. In mathematical terms, μ > 15

Question 3

Null hypothesis states that the price of the model of the car is not significantly different from $30,000. In mathematical terms,

μ = 30,000

Alternative hypothesis puts forward that the price of the model of the car is significantly greater than $30,000. In mathematical terms, μ > 30,000

Question 4

Null hypothesis maintains that proportion of Ann Arbor residents that are college students is 33%. In mathematical terms, p = 0.33

Alternative hypothesis will now be that the proportion of Ann Arbor residents that are college students is significantly greater than 33%. In mathematical terms, p > 0.33

Question 5

Null hypothesis maintains that the proportion of drivers in the United States who wear seat belts when driving is 84%. In mathematical terms, p = 0.84

Alternative hypothesis is that the proportion of drivers in the United States who wear seat belts when driving is significantly different from 84%. In mathematical terms, p ≠ 0.84

Hope this Helps!!!