Download Class Activity -Hypothesis Testing

Self- assessment exam C - Inferential Statistics -answers
Name: _____________________________________________________
Problem 1. A study was conducted to estimate the cost of health insurance in a certain city.
Twenty randomly selected families were selected and the sample showed a mean of $270 per
month with a standard deviation of $68 a month. The population of costs of health insurance can
be assumed to be normally distributed. Construct a 99% confidence interval for the average cost
of health insurance in that particular city.
a) Complete following list of values if they can be obtained from the given information
n  _____ ,   __________, x  ______, x  _______
s  ___ ,   _______, p  _______, p̂  ________,   ___
b) Write the formula for constructing the required confidence interval and substitute the values in
the formula.
answer: ______
c) We conclude with a 99% confidence that the true average cost of health insurance in that
particular city is between ________ per month ______ and _____ per month ______
d) We can assert with 99% confidence that maximum error of estimation is _____ per month
____
Problem 2 –.
A certain drug is used for the treatment of hypertension. In a clinical test, 9 of 250 users of the
drug experienced dizziness. Construct a 98% confidence interval estimate of the percentage of
all users of this drug who experience dizziness.
a) Give the following information if they can be obtained from the information of the problem.
n  _____ ,   __________, x  ________, x  9 ______
s  ______ ,   _______, p  _______, p̂  ______,   ___
b) Write the formula appropriate for constructing the required confidence interval and substitute
the values in the formula
Answer:
c) We conclude with a 98% of confidence that the proportion of the users of the drug who suffer
dizziness is between _______% and _______%. The error of estimation is ____ %
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Problem 3.
A certain drug is used for the treatment of hypertension. In a clinical test, 9 of 250 users of the
drug experienced dizziness. How large a sample is needed to construct a 98% confidence
interval estimate of the percentage of all users of this drug who experience dizziness if we want
to keep the error of estimation within 1.8% (0.018)
n  _____ , x  _____, x  ___ s  ___ , p  ___, p̂  ______,   ___
b) Write the formula appropriate for determining how large a sample is needed and substitute the
values in the formula. Use for p the estimated value 0.036
Answer:
__________________________________
c) ____users must be included in the pollster to be 98% confident and the poll to be accurate
within _____ points.
Problem 4: In a poll of 200 randomly selected students from a college 116 of them were in favor
of the death penalty for a certain person convicted of murder. Use the above information to test
at a 5% level of significance, the claim that the majority of the college students are in favor of
the death penalty for that person.
Step 1. Is this a hypothesis about p or  ? ________
n  ____,   ___ x  ___, s  ___,   ___, x ____, p̂  _____,   ____
H 0 : __________ H1 : _________
Step 2. Type of test – select: ________
a) two-tailed test
b) right-tailed test
c) left –tailed test ____________
Step 3. Level of significance: ______
Step 4. Find the p-value – Show the work.
Step 5. Compare the p-value with  . Select: ______
a) p-value < 
b) p-value > 
Step 6. Conclusion. Select: ______________________
a) We reject the null hypothesis
b) We fail to reject the null hypothesis
Select: ______________
a) There is not sufficient evidence at a 5% level to warrant rejection of the claim that the
majority of the college students are in favor of the death penalty for that person.
b) There is sufficient evidence at a 5% level to warrant rejection of the claim that the majority of
the college students are in favor of the death penalty for that person.
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Problem 5. The following sample for the emissions of nitrogen-oxide (in grams per mile) for
eight cars was obtained: 0.07, 0.11, 0.14, 0.13, 0.08, 0.16, 0.08, 0.10. Assume that the
population from which the sample was obtained is normally distributed.
If the Environmental Protection Agency requires that the average nitrogen-oxide emissions be
less than 0.164 grams/mile, can we safely conclude at a 5% level of significance that this
requirement is being met?
a) Complete the following information if it can be obtained from the statement of the problem.
n  ____,   ___ x  ______, s  _____,   ____, x  __ p̂  __,   ___
b) Test the hypothesis.
Is this a hypothesis about p or  ? ______
Step 1.
H 0 : _________ H1 : _________
Step 2. Type of test – select: _____________
a) two-tailed test
b) right-tailed test
c) left –tailed test ____________
Step 3. level of significance is _______
Step 4. Find the p-value – Show the work.
p-value = ___________
Step 5. Compare the p-value with  . Select: _______
a) p-value < 
b) p-value > 
Step 6.
Conclusion. Select: a____________________
a) We reject the null hypothesis
b) We fail to reject the null hypothesis
Conclusion: Select: __________________
a) We can safely conclude at a 5% level of significance that the Environmental Protection
Agency requirement that the average nitrogen-oxide emissions be less than 0.164 grams/mile, is
being met.
b) We can not safely conclude at a 5% level of significance that the Environmental Protection
Agency requirement that the average nitrogen-oxide emissions be less than 0.164 grams/mile, is
being met.
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