NEED STATISTICS HOMEWORK DONE BY SAT 4/27/2013 AT 9PM EASTERN TIME
Quiz 5
1. The mean weight of the adults in a certain region is believed to be . An agency thinks that this
mean may be higher than the above belief. They are going to take a simple random sample of 100 adults for a hypothesis test at 5% level of significance.
a) State the null and the alternate hypothesis for this test.
b) If the mean weight of the adults in the above simple random sample is and we know that the population standard deviation is , compute the test statistic and the P_value of the test.
c) Will you reject or not reject the null hypothesis at 5% level of significance?
2. An expensive medication from a particular company states 100 ml for the contents on the bottles for this medication. An agency would like to test if the bottles are being under filled, in the sense that the mean contents of all bottles is less than 100 ml.
a) State the null hypothesis and the alternative hypothesis.
b) The contents in 10 randomly selected bottles were measured, and the results are below in ml.
contents in ml
96.0 102.0 99.4 100.5 97.5 98.7 103.4 97.6 98.5 99.4
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3
contents 10 0 99.300 0.696 2.201 96.000 97.575 99.050 100.875
Variable Maximum
contents 103.400
State the test statistic
State the P_value.
Does this sample show a good evidence at 5% level of significance that the bottles are being under filled?
3. The electricity supply in a certain region appears to show a lot of voltage fluctuation from the required value of 240 V.
To check if the mean voltage is different from 240 V, the voltage will be measured at 15 randomly selected times.
a) State the null and the alternative hypothesis for this test.
b) The following are the readings shown by the 15 measurements.
voltage
222.2 217.9 211.9 219.7 208.8 229.5 219.4 208.1 209.0 208.2 196.2 211.7 199.9 201.1 218.0
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3
voltage 15 0 212.11 2.35 9.10 196.20 208.10 211.70 219.40
Variable Maximum
voltage 229.50
a) Write the test statistic.
b) Will you reject or not reject the null hypothesis at 5% level of significance?
c) Compute a 95% confidence interval for the overall mean voltage based on the results from the above sample.
d) Does this interval contain the value 240 Volt?
e) Explain the usage of a 95% confidence interval for a two sided hypothesis test for a population mean at a 5% level of significance.
4.
In the past, 44% of those taking a public accounting qualifying exam have passed the exam on their first try. Lately, the availability of exam preparation books and tutoring sessions may have improved the likelihood of an individual’s passing on his or her first try. To test if the likelihood of passing in the first try in now higher,
a simple random sample of recent applicants will be examined.
a) State the null hypothesis and the alternative hypothesis
b) In a sample of 250 recent applicants, 130 passed on their first attempt. At 0.05 level of significance, can we conclude that the proportion passing on the first try has increased? State the P_value and a reason for your conclusion.
5. We are testing
2
1
2
1
:
:
p
p
H
p
p
H
A
o
¹
=
at 1% level of significance for the presence of an attribute in two populations 1 and 2.
The results from independent simple random samples are shown below.
Population 1
Population 2
# with the attribute
56
198
Sample size
132
489
a) State the test statistic, the P_value, and your conclusion about rejecting or not rejecting the null hypothesis.
b) Compute a 99% confidence interval for
2
1
p
p
=
and describe whether the information from this interval is consistent with the conclusion in the hypothesis test.
6. Explain the meaning of a type I error and a type II error.
7. We are going to test the null and the alternative hypotheses
80
:
80
:
0
>
=
m
m
A
H
H
based on a simple random sample of size 50 and the population standard deviation
20
=
s
a) Compute the probability of a type II error if actually
84
=
m
b) Compute the power of the test if actually
84
=
m
c) Compute the probability of a type II error if actually
90
=
m
d) Compute the power of the test if actually
90
=
m
8. (a review question)
Two fair dice are rolled and the number of dots facing up is added.
a) Find the probability that the sum of the dots facing up is 7.
b) Find the probability that the sum of the dots facing up is 11.
c) A game charges you a $1 to play and lets you roll a pair of fair dice. It pays $3.00 (i.e. a profit of $2.00)
if the sum of the dots facing up is 7 or 11, otherwise
does not pay any money back.
Fill in the following table
# of dots facing up
Gain
Probability
7,11
2
2,3,4,5,6,8,9,10,12
─1
d) What is the expected value of this game?
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