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Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset Vaia Explanations$ Math

OER 2018 Edition · 902 pages

ISBN: 9781938168208

Chapter 9: Q.53 (page 539)

Draw the graph of a two-tailed test.

Short Answer

Expert verified

A two-tailed test results from an alternative hypothesis that does not specify a direction. A two-tailed test has two critical regions.

Step by step solution

01

Diagram

A Diagram showing a two-tailed test.

02

Explanation

A two-tailed test signifies that we're looking for an area in the middle of the distribution. Alternatively, your rejection region ( where one rejects the null hypothesis) is on both ends of the tails.

A two-tailed test is required when the degree of uncertainty cannot be known on the higher or lower side.

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Most popular questions from this chapter

La Leche League International reports that the mean age of weaning a child from breastfeeding is age four to five worldwide. In America, most nursing mothers wean their children much earlier. Suppose a random survey is conducted of 21 U.S. mothers who recently weaned their children. The mean weaning age was nine months (3/4 year) with a standard deviation of 4 months. Conduct a hypothesis test to determine if the mean weaning age in the U.S. is less than four years old.

The National Institute of Mental Health published an article stating that in any one-year period, approximately $9.5$ percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population.

a. Is this a test of one mean or proportion?

b. State the null and alternative hypotheses.

$H_{0} :$

$H_{a} :$

c. Is this a right-tailed, left-tailed, or two-tailed test?

d. What symbol represents the random variable for this test?

e. In words, define the random variable for this test.

f. Calculate the following:

i. $x =$

ii.role="math" localid="1649760873126" $n =$

iii. $p^{'} =$

g. Calculate role="math" localid="1649760901479" $σ_{x} =$ Show the formula set-up.

h. State the distribution to use for the hypothesis test.

i. Find the $p$ -value.

j. At a pre-conceived $α = 0.05$ , what is your:

i. Decision:

ii. Reason for the decision:

iii. Conclusion (write out in a complete sentence):

Some of the following statements refer to the null hypothesis, some to the alternate hypothesis. State the null hypothesis, $H 0$ , and the alternative hypothesis. Ha, in terms of the appropriate parameter $(μ o r p)$ .

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 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.

Driver error can be listed as the cause of approximately $54 %$ of all fatal auto accidents, according to the American Automobile Association. Thirty randomly selected fatal accidents are examined, and it is determined that $14$ were caused by driver error. Using $α = 0.05,$ is the AAA proportion accurate?

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 $(=, \neq, \geq, \leq, \leq, >)$ for the null and alternative hypotheses.

a. $H_{0} : μ_{-} 45$

b. $H_{a} : μ - 45$

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