Two sample Tests &
Intervals on the
Calculator
Two independent random samples of women’s clubs in a particular city
are taken in order to determine the average amount of time the members
spend volunteering. Fifteen garden club members spent an average of
17.25 days with a standard deviation of 2.4 days. The mean of 12 library
members was 16.45 with a standard deviation of 3.6. Construct a 90%
confidence interval for the difference in volunteering time.
What kind of Interval? (Use formula)
Interval:
Result:
In a fast food study, a researcher finds that the mean sodium content of
42 Wendy’s fish sandwiches is 1010 milligrams with a standard deviation
of 75 mg. The mean sodium content of 39 Long John silver’s fish
sandwiches is 1180 mg with a standard deviation of 90 mg. Is there
enough evidence fore the researcher to conclude that the Wendy’s fish
sandwich has less sodium than the Long John Silver’s fish sandwich?
The guidance dept. wants to see if a new SAT prep program
will improve their SAT scores by at least 50 points. Ten
members of the junior class were selected. Results are
below. Test the claim.
Stud
1
2
3
4
5
6
7
8
9
10
Bef
475
512
494
465
523
560
610
477
501
410
After
500
540
512
530
533
603
691
512
489
458
A real estate agent claims that there is no difference between the mean
household incomes of two neighborhoods. The mean income of 12
randomly selected households from the first neighborhood was $32,750
with a standard deviation of $1900. In the second neighborhood, 10
randomly selected households had a mean income of $31,200 with a
standard deviation of $1825. Create a 95% confidence interval of the
difference in mean household incomes of the two neighborhoods.
In a random sample of 800 US adults, 38% are worried that they are
someone in their family will become a victim of terrorism. In another
random sample of 1100 US adults taken a month earlier, 42% were worried
that someone in their family would become a victim of terrorism. At a 10%
level of significance, test the claim that the proportion has changed.
In a survey of 900 US adults in 2008, 468 considered the amount
of federal income tax they had to pay to be too high. In a recent
year, in a survey of 1027 U.S. adults 472 considered the amount
too high. Create a 90% confidence interval of the difference in the
proportion who believed that the income tax amount was too
high.
Which of the following is true about
constructing confidence intervals?
A.
B.
C.
D.
E.
The value of the standard error is a function of the
sample statistics.
The center of the confidence interval is the
population parameter.
One of the values that affects the width of a
confidence interval is the sample size.
If the value of the population parameter is know, it
is irrelevant to calculate a confidence interval for it.
The value of the level of confidence will affect the
width of a confidence interval.
The confidence that we feel about a 90%
confidence interval comes from the fact that
A.
B.
C.
D.
E.
There is a 90% chance that the population
parameter is contained in the confidence interval.
There is a 90% chance that the sample statistic is
contained in the confidence interval.
90% of confidence intervals constructed around a
sample statistic will contain the population
parameter.
The terms of confidence and probability are
interchangeable.
The concepts of confidence and probability are
synonymous.
If the 95% confidence interval of the proportion of
a population is 0.35 ±0.025, which of the following
are true?
A.
B.
C.
D.
E.
If the sample size were to increase the width of the
interval would decrease.
An increase in confidence level generally results in an
increase in the width of the confidence interval.
If one would like a smaller confidence interval, one
could increase sample size or decrease the confidence
level.
This confidence interval could have been calculated
after either a sample or a census was conducted.
If 1,000 samples of the same size are taken from a
population, then approximately 900 will contain the
sample mean.
What sample size is needed to be within 2.5% of
the true proportion of approval votes at the 98%
confidence level.
A preliminary study has indicated that the standard
deviation of a population is approximately 7.85 hours.
Determine an appropriate sample size if the estimate of the
population mean is to be within 2 hours at the 95%
confidence level?
Homework
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Worksheet
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Identify the hypothesis
Give the formula
Give the test statistic
Give the p-value
State the decision