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1. In own words explain the difference between a point estimate and an interval
estimate of a parameter? Which is better? Why?
Point estimate is a single value estimated for a population parameter. Interval estimate is
an interval estimated for a population parameter. Actually a single value estimate is not
reasonable, because we can not exactly estimate a population parameter from a limited
number sample. An interval estimate is a better estimate of what a parameter could be.
2. What information is necessary to calculate a confidence interval? Is the size of the
population relevant when one is determining the sample size for a confidence
interval? What is necessary to determine the sample size?
The information needed to calculate a confidence interval include the degrees of freedom,
level of confidence, t-distribution probability that corresponds to confidence level, tail
information, and the population mean difference on both ends of the confidence interval.
The sample size is very significant when using interval estimates because the larger the
sample the more information about the population one receives and can make a more
precise interval. You must have confidence level, allowable sampling error, degree of
variability, and be aware of population size
3. Choose a variable (such as number of daily admissions at a local theater or
number of miles students have to commute daily to get to their college.) Before
collecting the data, decide what a likely average might be, then complete the
following:
a. Write a brief statement of purpose of the study
b. Define the population
c. State the hypotheses for the study
d. select a value
e. State how the sample was selected
f. Show the raw data
g. Compute the test statistic
h. Find the critical values(s)
i. State the decision
j. Summarize the results
Variable chosen: number of daily admissions at a local theater.
A likely average may be 56.
a) Purpose of this study is to define the sample and population, state the null and
alternative hypotheses, collect relevant representative data, apply the appropriate
hypothesis testing algorithm, and prove any difference from the stated population
parameter.
b) Population is daily admissions at all theaters in the U.S.
c) H0: μ = 56 (Average number of daily admissions is 56)
Ha: μ ≠ 56 (Average number of daily admissions is different than 56)
d) Significance level is 5% so α=0.05 (which is typical for hypothesis testing)
e) Random samples are obtained by giving a number to each theater and then selecting
among them by using a random number table.
f) 54, 60, 49, 57, 61, 56, 60, 47
g) Mean = 55.5 and standard deviation = 5.21 calculated from the raw data
55.5  56
 0.27
5.21
(
)
8
Test statistic =
h) Critical t values are -2.365 and 2.365 found from t distribution table with df =7.
i) Since test statistic is between the critical values, we fail to reject the null hypothesis
j) We don't have sufficient evidence to conclude that the average daily admissions is
different than 56.