9.1 Null and Alternative Hypotheses

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 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% 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 student loan recipients revealed that the mean length of time in repayment 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 in repayment 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% of Americans vote in presidential elections.
3. The mean starting salary for San Jose State University graduates is a…

A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening night midnight showing of the latest Marvel Universe movie. The instructor surveys 84 students and finds that 11 attended the midnight showing. An appropriate alternative hypothesis is:

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