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STAT 1450 Chapter Notes - Chapter 20: Confidence Interval, Statistic, Sampling Distribution

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Ohio State University
Department
Statistics
Course
STAT 1450
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All

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Document Summary

The inference we did in chapters 14-18 revolved around the population mean. If we want to do inference about the proportion of some outcome in a population, we can use similar processes with appropriate changes. As before, we want to use a sample statistic to estimate a population parameter. Here our sample statistic is the sample proportion: P = number of successes in the sample total number of individuals in the sample. We use the sample proportion p to estimate the population proportion p. The number of successes in the sample is the number of times the event of interest happens. Explain to the students that sometimes a success is not a good thing (e. g. , death but if we are interested in the proportion of deaths, death is a success ). Draw an srs of size n from a large population that contains proportion p of successes. Let p be the sample proportion of successes,

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

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Related Questions

6. As the test statistic becomes larger, the p-value

(a) gets smaller

(b) becomes larger 

(c) stays the same, since the sample size has not been changed

(d) becomes negative.

 

7. To describe the sampling distribution of the sample proportion, we use

(a) The sample proportion 

(b) The population proportion 

(c) The population mean

(d) The population mean

 

8. When small samples are used to estimate a population mean, in cases where the population standard deviation is unknown and the original distribution is normal:

(a) There always will be a large amount of sampling error.

(b) the t-distribution must be used to obtain the critical value.

(c) the resulting margin of error for a confidence interval estimate will tend to be fairly small.

(d) the z distribution must be used to obtain the critical value.

 

 

Which of the following is NOT true when testing a claim about a​proportion?

A. If you want to test a claim about population​ proportions, use the​ P-value method or the classical method of hypothesis testing.

B. When testing claims about population​ proportions, the traditional method and the​ P-value method are equivalent in the sense that they always yield the same result.

C. A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test.

D. Both the traditional method and​ P-value method use the same standard deviation based on the claimed proportion​ p, but the confidence interval uses an estimated standard deviation based on the sample proportion ModifyingAbove p with caretp.

1. Matt, the manager, wants to estimate the mean wait time for customers to check out in his Mini-Market. He randomly selects customers and determines the mean wait time is minutes. Define the following for this exercise:

a) Is the data collected qualitative or quantitative?

b) Variable (x):

c) Population of Interest:

d) Sample:

e) Parameter of Interest and Statistic: Do you expect the parameter and the statistic to be the same value? Explain.

f) Discuss the use of descriptive and inferential statistics in this exercise.

g) Is the variable, x, discrete or continuous?

 

2. Identify the population and sample for the following examples:

The P.E. coach of a middle school interested in the mean height for the graders in the school. He randomly selects graders and measures the height of each.

a) Population:

b) 7thgraders Sample:

c) A community college notices that an increasing number of full-time students are working while attending school. The administration randomly selects 200 students and determines how many hours per week each student works.