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Chapter 7: Q108S (page 441)

Specify the differences between a large-sample and a small-sample test of a hypothesis about a population mean m. Focus on the assumptions and test statistics.

Short Answer

Expert verified

A large-sample, as well as a small-sample hypothesis test of a population, mean, 渭vary because a large sample can be considered to be typically disturbed.

Step by step solution

01

Hypothesis

A hypothesis is an assumption formed based on facts. This is the first step in every inquiry that converts research issues into forecasts. It consists of variables, a population, as well as the relationship among the variables. A research hypothesis is a theory used to evaluate the link among two or more variables.

02

Explanation

In a population's large-sample and small-sample hypothesis tests, the mean varies because a large sample can be considered typically disturbed. As a result, one can use a normally distributed area to conduct an extensive sample hypothesis test. However, this assumption may not remain valid for a smaller sample. Therefore we utilize the t distribution for a minor sample hypothesis test.

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Most popular questions from this chapter

Which hypothesis, the null or the alternative, is the status-quo hypothesis? Which is the research hypothesis?

Customers who participate in a store鈥檚 free loyalty card program save money on their purchases but allow the store to keep track of the customer鈥檚 shopping habits and potentially sell these data to third parties. A Pew Internet & American Life Project Survey (January 2016) revealed that 225 of a random sample of 250 U.S. adults would agree to participate in a store loyalty card program, despite the potential for information sharing. Letp represent the true proportion of all customers who would participate in a store loyalty card program.

a. Compute a point estimate ofp

b. Consider a store owner who claims that more than 80% of all customers would participate in a loyalty card program. Set up the null and alternative hypotheses for testing whether the true proportion of all customers who would participate in a store loyalty card program exceeds .8

c. Compute the test statistic for part b.

d. Find the rejection region for the test if 伪=.01.

e. Find the p-value for the test.

f. Make the appropriate conclusion using the rejection region.

g. Make the appropriate conclusion using the p-value.

7.83 A random sample of n observations is selected from a normal population to test the null hypothesis that 蟽2=25 . Specify the rejection region for each of the following combinations of Ha,伪and n.

a.Ha:蟽2鈮�25;伪=0.5;n=16

b. Ha:蟽2>25;伪=.01;n=23

c. Ha:蟽2>25;伪=.10;n=15

d. Ha:蟽2<25;伪=.01;n=13

e. Ha:蟽2鈮�25;伪=.10;n=7

f.Ha:蟽2<25;伪=.05;n=25

Improving the productivity of chickens. Refer to the Applied Animal Behaviour Science (October 2000) study of the color of string preferred by pecking domestic chickens, Exercise 6.124 (p. 376). Recall that n = 72 chickens were exposed to blue string and the number of pecks each chicken took at the string over a specified time interval had a mean of\(\overline x = 1.13\,\)pecks and a standard deviation of s = 2.21 pecks. Also recall that previous research had shown that m = 7.5 pecks if chickens are exposed to white string.

a. Conduct a test (at\(\alpha = 0.01\)) to determine if the true mean number of pecks at blue string is less than\(\mu = 7.5\)pecks.
b. In Exercise 6.122, you used a 99% confidence interval as evidence that chickens are more apt to peck at white string than blue string. Do the test results, part a, support this conclusion? Explain

Intrusion detection systems. The Journal of Research of the National Institute of Standards and Technology (November鈥� December 2003) published a study of a computer intrusion detection system (IDS). The IDS is designed to provide an alarm whenever unauthorized access (e.g., an intrusion) to a computer system occurs. The probability of the system giving a false alarm (i.e., providing a warning when no intrusion occurs) is defined by the symbol 伪, while the probability of a missed detection (i.e., no warning given when an intrusion occurs) is defined by the symbol 尾. These symbols are used to represent Type I and Type II error rates, respectively, in a hypothesis-testing scenario

a. What is the null hypothesis, H0?

b. What is the alternative hypothesis,Ha?

c. According to actual data collected by the Massachusetts Institute of Technology Lincoln Laboratory, only 1 in 1,000 computer sessions with no intrusions resulted in a false alarm. For the same system, the laboratory found that only 500 of 1,000 intrusions were actually detected. Use this information to estimate the values of 伪and 尾.
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