Practice Problems for Onesample Inference — Hypothesis Testing
© 2010 Radha Bose FSU Department of Statistics
1
1.
Ten brands of vanilla icecream had a mean of 131 cal/serving.
We want to know if this is evidence that
the mean caloric content of all brands of vanilla icecream is less than 140 cal/serving.
Assume that the
population of vanilla icecream caloric contents has standard deviation 30 cal/serving.
(a) Conduct an appropriate hypothesis test using the Pvalue approach
, detail all the steps and use
1
.
0
=
α
.
(b) Interpret the Pvalue in this context.
2.
Researchers collected a sample of 24 Florida alligators and found that their mean length was 130.6
inches.
The researchers want to know if the mean length of all Florida alligators is less than 144 inches.
The sample of alligators' lengths had standard deviation 19 inches.
(a) Conduct an appropriate hypothesis test using the Pvalue approach
, detail all the steps and use
0.05
α
=
.
(b) Interpret the Pvalue in this context.
3.
A random sample of 100 small businesses made a mean profit of $4000 (i.e. $4000 loss) in the last
financial year.
We want to know if this is any indication that the mean profit made by all small businesses
in the last financial year was greater than $10,000 (i.e. less than $10,000 loss).
(a) Conduct an appropriate hypothesis test using the Pvalue approach
, detail all the steps and use
0.05
α
=
.
Studies show that the standard deviation of profits made by small businesses in general is
around $27,800.
(b) Interpret the Pvalue in this context.
4.
An athlete's resting heart rate was measured 9 times during an active rest day.
These measurements
had mean 46 bpm and standard deviation 1.8 bpm.
Based on these data, can we say that her overall mean
resting heart rate is higher than 45 bpm?
(a) Conduct an appropriate hypothesis test using the Pvalue approach
, detail all the steps and use
01
.
0
=
α
.
(b) Interpret the Pvalue in this context.
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Practice Problems for Onesample Inference — Hypothesis Testing
© 2010 Radha Bose FSU Department of Statistics
2
5.
Thirty randomly selected types of calculators had a mean cost of $200.
The population distribution of
all such costs has standard deviation of $45.
We want to know if the sample data indicate that the mean
cost of all types of calculators is different from $180.
Conduct an appropriate hypothesis test using the
Pvalue approach
, detail all the steps and use
0.01
α
=
.
6.
Fortyfive employees at a certain hospital spent a mean of $9.50 at the hospital cafeteria.
We want
to know if this indicates that the mean amount spent at the cafeteria by all the hospital's employees is
not $10.
Conduct an appropriate hypothesis test using the Pvalue approach
, detail all the steps and use
0.1
α
=
.
The standard deviation of the amounts spent by the sample of employees was $1.96.
7.
Sixty bicyclists took a mean of 34.8 mins to finish a race.
We wish to know if these observations
indicate that, for all bicyclists who might enter this particular race, the mean finishing time would be less
than 40 mins.
In general, the finishing times for this race vary with standard deviation 12.5 mins.
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 Fall '11
 RADHABOSE
 Statistics, Statistical hypothesis testing, Radha Bose FSU Department of Statistics, Radha Bose FSU, Bose FSU Department

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