Spring 2010
Math 227
Test #3
Name: _____________________________
Instruction: For hypothesis testing, you may use the traditional method or the P-value method, but you need to
show all the steps. For confidence intervals for proportion or mean, you will need to find the critical value, margin
of error, then the confidence interval. (Total: 75 points)
1.
A survey of 935 randomly selected Americans, 60% of the sample answered “yes” to the question “Do you
think there is intelligent life on other planets?” Construct a 90% confidence interval for the proportion of all
Americans who believe that there is intelligent life on other planets.
Critical Value: _______________
(8)
Margin of Error: ________________
Confidence Interval: __________________
2.
(9)A
sample of 36 vacation homes build during the past 2 years in a coastal resort region gave a mean
construction cost of $159,000 and standard deviation of $27,000.
a. (1) What is the point estimate of the corresponding population mean?
b. Construct a 99% confidence interval for the mean construction cost for all vacation homes built in this
region during the past 2 years.
Critical Value: _______________
Margin of Error: __________________
Confidence Interval: ____________________
3.
(6)An
economist wants to find a 90% confidence interval for the mean sale price of houses in a state. How large
a sample should she select so that the estimate is within $3500 of the population mean? Assume that the
standard deviation for the sale prices of all houses in this state is $31,500.
1
4.
(10) As
noted in U.S. Senate Resolution 28, 9.3% of Americans speak their native language and another language
fluently. Suppose that in a recent sample of 880 Americans, 69 speak their native language and another
language fluently. Is there significant evident that the percentage of all Americans who speak their native
language and another language fluently is different from 9.3%? Using 𝛼 = 0.05.
5.
(6) An
office supply company conducted a survey before marketing a new paper shredder designed for home use.
In the survey, 80% of the people who tried the shredder were satisfied with it. Assume that 80% of all people
are satisfied with this shredder. During a certain month, 100 customers bought this shredder, use normal
approximate to binomial to find the probability that of these 100 customers, the number who is satisfied is at
most 73.
2
6.
(8)The
listed values are waiting times (in minutes) of customers at the Jefferson Valley Bank, where customers
enter a single waiting line that feeds three teller windows. Construct a 99% confidence interval for the
population standard deviation.
6.5
6.6
6.7
6.8
7.1
7.3
7.4
7.7
7.7
7.7
Mean of the sample: ___________
Standard deviation of the sample: _______________
Critical Values: ________________________
Confidence interval: _____________________________
7.
(6) Identifying
Hypotheses. Write the null hypothesis and alternative hypothesis in symbolic form.
a. Claim: The mean annual income of full-time students is below $10,000.
b. Claim: The majority of college students have at least one credit card.
c. Claim: Statistics professors have IQ scores that vary less than IQ scores from the adult population, which has
standard deviation of 15.
8.
(6) Assume
that the weights of all packages of a certain brand of cookies are normally distributed with a mean of
32 ounces and a standard deviation of 0.3 ounce. Find the probability that the mean weight of a random sample
of 20 packages of this brand of cookies will be at least 31.8 ounces.
3
9.
(6)A
college registrar has received numerous complaints about the online registration procedure at her college,
alleging that the system is slow, confusing, and error prone. She wants to estimate the proportion of all
students at this college who are dissatisfied with the online registration procedure. A preliminary study has
shown that 70% of the students surveyed at this college are dissatisfied with the current online registration
system. How large a sample should be taken in this case so that the margin of error is within 0.05 of the
population proportion for a 90% confidence interval?
10.
(10) A
sample of 106 body temperatures with a mean of 98.20℉. Assume that 𝜎 is known to be 0.62℉. use a
0.05 significance level to test the claim that the mean body temperature of the population is less than 98.60℉.
4