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Chapter 9: Q.29 (page 538)

You are performing a hypothesis test of a single population proportion. What must be true about the quantities of np and nq?

Short Answer

Expert verified

When running a single population proportion hypothesis test, make sure the numbers (p)and (q) are more than five to ensure the binomial distribution follows the normal distribution.

Step by step solution

01

Given Information

While performing a hypothesis test of a single population percentage, I must specify what should be true about amounts of (p)and (q) based on the facts. Typically, a hypothesis test is conducted on a sample of data drawn from a broader population. This test is used to generate results from sample data based on a hypothesis. This test is usually used by analysts to see if their hypothesis is correct or incorrect. The binomial distribution is a type of probability distribution in which the value might take one of two values based on a set of assumptions. This strategy involves n trials, each of which will result in one of two outcomes: success or failure.

02

Explanation

While performing a hypothesis test of a single population proportion one must take care that the quantities are greater than five because the resultant curve will be normal only when ((and (q are greater than five. Always binomial distribution should follow normal distribution therefore the quantities should always be in the following proportion : p>5andq>5.

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Most popular questions from this chapter

For statements a-j ( Section: 9.109 ), answer the following in complete sentences.

a. State a consequence of committing a Type I error.

b. State a consequence of committing a Type II error.

State the Type I and Type II errors in complete sentences given the following statements.

a. The mean number of years Americans work before retiring is 34.

b. At most 60% of Americans vote in presidential elections.

c. The mean starting salary for San Jose State University graduates is at least \(100,000 per year.

d. Twenty-nine percent of high school seniors get drunk each month.

e. Fewer than 5% of adults ride the bus to work in Los Angeles.

f. The mean number of cars a person owns in his or her lifetime is not more than ten.

g. About half of Americans prefer to live away from cities, given the choice.

h. Europeans have a mean paid vacation each year of six weeks.

i. The chance of developing breast cancer is under 11% for women.

j. Private universities mean tuition cost is more than \)20,000 per year.

Use the following information to answer the next seven exercises: Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. A study was then done to see if the mean time has increased in the new century. A random sample of 26 first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was three years with a standard deviation of 1.8 years. Suppose that it is somehow known that the population standard deviation is 1.5. Conduct a hypothesis test to determine if the mean length of jail time has increased. Assume the distribution of the jail times is approximately normal.

Calculate the following:

a. X炉 _______

b. 蟽 _______

c.Sx _______

d.n_______

Refer to Exercise 9.119. Conduct a hypothesis test to see if your decision and conclusion would change if your belief were that the brown trout's mean I.Q is not four.

According to the Center for Disease Control website, in 2011 at least 18% of high school students have smoked a cigarette. An Introduction to Statistics class in Davies County, KY conducted a hypothesis test at the local high school (a medium sized鈥揳pproximately 1,200 students鈥搒mall city demographic) to determine if the local high school鈥檚 percentage was lower. One hundred fifty students were chosen at random and surveyed. Of the 150 students surveyed, 82 have smoked. Use a significance level of 0.05 and using appropriate statistical evidence, conduct a hypothesis test and state the conclusions.
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