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Chapter 8: Problem 1

Briefly explain the meaning of an estimator and an estimate.

Short Answer

Expert verified
An estimator is a rule or a statistical method used to calculate parameter values (like a recipe), while an estimate is the actual numerical value obtained by applying this rule to specific data (like the cooked dish).

Step by step solution

01

Define 'Estimator'

An 'estimator' is a rule or a statistical method that is used to calculate the values of a parameter of interest. It is typically a function of the sample data, and they are often denoted by a '^' symbol.
02

Define 'Estimate'

An 'estimate' is the actual numerical value obtained by using an estimator with a specific set of data. It is a single realization of the estimator.
03

Understand the relationship between 'Estimator' and 'Estimate'

The relationship between an estimator and an estimate can be compared to that of a recipe and a cooked dish. Estimators are the recipes or methods that give instructions on how to calculate the parameters, whereas the estimates are the final outcomes or the cooked dishes obtained by applying these recipes/ methods to sample data.

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Most popular questions from this chapter

A large city with chronic economic problems is considering legalizing casino gambling. The city council wants to estimate the proportion of all adults in the city who favor legalized casino gambling. What is the most conservative estimate of the minimum sample size that would limit the margin of error to be within \(.05\) of the population proportion for a \(95 \%\) confidence interval?

A random sample of 36 mid-sized cars tested for fuel consumption gave a mean of \(26.4\) miles per gallon with a standard deviation of \(2.3\) miles per gallon. a. Find a \(99 \%\) confidence interval for the population mean, \(\mu\). b. Suppose the confidence interval obtained in part a is too wide. How can the width of this interval be reduced? Describe all possible alternatives. Which alternative is the best and why?

You are working for a supermarket. The manager has asked you to estimate the mean time taken by a cashier to serve customers at this supermarket. Briefly explain how you will conduct this study. Collect data on the time taken by any supermarket cashier to serve 40 customers. Then estimate the population mean. Choose your own confidence level.

A hospital administration wants to estimate the mean time spent by patients waiting for treatment at the emergency room. The waiting times (in minutes) recorded for a random sample of 35 such patients are given below. The population standard deviation is not known. \(\begin{array}{rrrrrrr}30 & 7 & 68 & 76 & 47 & 60 & 51 \\ 64 & 25 & 35 & 29 & 30 & 35 & 62 \\ 96 & 104 & 58 & 32 & 32 & 102 & 27 \\ 45 & 11 & 64 & 62 & 72 & 39 & 92 \\ 84 & 47 & 12 & 33 & 55 & 84 & 36\end{array}\) Construct a \(99 \%\) confidence interval for the corresponding population mean.

Check if the sample size is large enough to use the normal distribution to make a confidence interval for \(p\) for each of the following cases. a. \(n=50 \quad\) and \(\quad \hat{p}=.25\) b. \(n=160\) and \(\hat{p}=.03\) c. \(n=400\) and \(\hat{p}=.65\) d. \(n=75 \quad\) and \(\quad \hat{p}=.06\)
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