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Which of the elements of a test of hypothesis can and should be specified prior to analyzing the data that are to be used to conduct the test

Short Answer

Expert verified

The elements of a test of hypothesis can and should be specified prior to analyzing the data that are to be used to conduct the test are null hypothesis, alternative hypothesis, test statistic, and rejection region.

Step by step solution

01

Given information

The information regarding the test hypothesis.

The test hypothesis can be used to conduct the test.

02

State the statistical hypothesis test

Hypothesis testing is a method in which statistical data from a group sample is drawn to reach a conclusion about population parameters. Generally, it is used when you want to compare two or more groups.

03

Explain the elements of a test hypothesis used to conduct the test prior to analyzing the data

Before performing any test of hypothesis, we must specify the null and alternative hypothesis as well as the desired level of significance α.

The given four elements are specified before the sampling experiment is performed.

Null Hypothesis (H0):

The null hypothesis is the theory about the specific values of one or more population parameters. The theory is always stated as H0: parameter=value.

Alternative Hypothesis (Ha):

The alternative hypothesis is a theory that contradicts the null hypothesis. The theory represents that which we will adopt only when sufficient evidence exists to establish its truth.

Test statistic:

A sample statistic is used to decide whether to reject the null hypothesis.

Rejection region:

The numerical values of the test statistic for which the null hypothesis will be rejected.

Hence, the elements of a test of hypothesis can and should be specified prior to analyzing the data that are to be used to conduct the test are null hypothesis, alternative hypothesis, test statistic, and rejection region.

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Most popular questions from this chapter

Libor interest rate. The interest rate at which London banks lend money to one another is called the London interbank offered rate, or Libor. The British Bankers Association regularly surveys international banks for the Libor rate. One recent report (Bankrate.com, March 16, 2016) had the average Libor rate at 1.2% for 1-year loans—a value considered high by many Western banks. Set up the null and alternative hypotheses for testing the reported value.

Ages of cable TV shoppers. Cable TV’s Home Shopping Network (HSN) reports that the average age of its shoppers is 52 years. Suppose you want to test the null hypothesis,\({H_0}:\mu = 52\), using a sample of\(n = 50\) cable TV shoppers.

a. Find the p-value of a two-tailed test if\(\overline x = 53.3\)and\(s = 7.1\)

b. Find the p-value of an upper-tailed test if\(\overline x = 53.3\)and\(s = 7.1\)

c. Find the p-value of a two-tailed test if\(\overline x = 53.3\)and\(s = 10.4\)

d. For each of the tests, parts a–c, give a value of\(\alpha \)that will lead to a rejection of the null hypothesis.

e. If\(\overline x = 53.3\), give a value of s that will yield a two-tailed p-value of 0.01 or less.

a. List three factors that will increase the power of a test.

b. What is the relationship between b, the probability of committing a Type II error, and the power of a test?

Refer to Exercise 7.99.

a. Find b for each of the following values of the population mean: 74, 72, 70, 68, and 66.

b. Plot each value of b you obtained in part a against its associated population mean. Show b on the vertical axis and m on the horizontal axis. Draw a curve through the five points on your graph.

c. Use your graph of part b to find the approximate probability that the hypothesis test will lead to a Type II error when m = 73.

d. Convert each of the b values you calculated in part a to the power of the test at the specified value of m. Plot the power on the vertical axis against m on the horizontal axis. Compare the graph of part b with the power curve of this part.

e. Examine the graphs of parts b and d. Explain what they reveal about the relationships among the distance between the true mean m and the null hypothesized mean m0, the value of b, and the power.

If the rejection of the null hypothesis of a particular test would cause your firm to go out of business, would you want ato be small or large? Explain

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