9.1 Null and Alternative Hypotheses

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25 percent. State the null and alternative hypotheses.

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

1. H₀: μ __ 66
2. H_a: μ __ 66

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

1. H₀: μ __ 45
2. H_a: μ __ 45

On a state driver’s test, about 40 percent pass the test on the first try. We want to test if more than 40 percent pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

1. H₀: p __ 0.40
2. H_a: p __ 0.40

You are testing that the mean speed of your cable internet connection is more than three megabits per second. What is the random variable? Describe it in words.

The American family has an average of two children. What is the random variable? Describe in words.

A sociologist claims the probability that a person picked at random in Times Square in New York City is visiting the area is 0.83. You want to test to see if the proportion is actually less. What is the random variable? Describe in words.

In a population of fish, approximately 42 percent are female. A test is conducted to see if, in fact, the proportion is less. State the null and alternative hypotheses.

A random survey of 75 long-term marathon runners revealed that the mean length of time they've been running is 17.4 years with a standard deviation of 6.3 years. If you were conducting a hypothesis test to determine if the population mean time for these runners could likely be 15 years, what would the null and alternative hypotheses be?

1. H₀: __________
2. H_a: __________

Some of the following statements refer to the null hypothesis, some to the alternate hypothesis.

State the null hypothesis, H₀, and the alternative hypothesis. H_a, in terms of the appropriate parameter (μ or p).

1. The mean number of years Americans work before retiring is 34.
2. At most 60 percent of Americans vote in presidential elections.
3. The mean starting salary for San Jose State University graduat…

A statistics instructor believes that fewer than 20 percent of Evergreen Valley College (EVC) students attended the opening night midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 attended the midnight showing. An appropriate alternative hypothesis is as follows:

1. p = 0.20
2. p > 0.20
3. p < 0.20
4. p ≤ 0.20