A company believes that it controls more than 30% of the total market
share for one of its products. To prove this belief, a random sample of 144
purchases of this product is contacted. It is found that 50 of the 144
purchased this company’s brand of the product. If a researcher wants to
conduct a statistical test for this problem, the alternative hypothesis would
be ________.
the population proportion is less than 0.30.
the population proportion is greater than 0.30
the population proportion is not equal to 0.30
the population mean is less than 40
the population mean is greater than 40
The number of phone calls arriving at a switchboard in a 10 minute time
period would best be modeled with the ________.
binomial distribution
hypergeometric distribution
Poisson distribution
hyperbinomial distribution
exponential distribution
Hope Hemandez, Marketing Manager of People’s Pharmacy, Inc., wants a
regression model to predict sales in the greeting card department. Her
data set includes two qualitative variables: the pharmacy eighborhood
(urban, suburban, and rural), and lighting level in the greeting card
department (soft, medium, and bright). The number of dummy variables
needed for Hope’s regression model is ________.
2
4
6
8
9
You want to build the regression model, the following scatter plot indicates
________.
a log x transform may be useful
a log y transform may be useful
an x2 transform may be useful
no transform is needed
a (−x) transform may be useful
You want to build the regression model, the following scatter plot indicates
________.
a x2 transform may be useful
a log y transform may be useful
a x4 transform may be useful
no transform is needed
a x3 transform may be useful
Jessica Salas, president of Salas Products, is reviewing the warranty policy
for her company’s new model of automobile batteries. Life tests performed
on a sample of 100 batteries indicated: An average life of 75 months, a
standard deviation of 5 months, and a bell shaped battery life distribution.
What percentage of the batteries will fail within the first 65 months of use?
(5)
Abel Alonzo, Director of Human Resources, is exploring employee
absenteeism at the Plano Power Plant. Ten percent of all plant employees
work in the finishing department; 20% of all plant employees are absent
excessively; and 7% of all plant employees work in the finishing
department and are absent excessively. A plant employee is selected
randomly; F is the event “works in the finishing department;” and A is the
event “is absent excessively.” P(A|F) = (6) .
Circuit boards for wireless telephones are etched, in an acid bath, in
batches of 100 boards. A sample of seven boards is randomly selected from
each lot for inspection. A particular batch contains two defective boards;
and x is the number of defective boards in the sample. P(x = 0) is (7) .
Sure Stone Tire Company has established that the useful life of a
particular brand of its automobile tires is normally distributed with a
mean of 40,000 miles and a standard deviation of 5000 miles. What is the
probability that a randomly selected tire of this brand has a life between
30,000 and 50,000 miles? (8)
James Desreumaux, VP of Human Resources of American First Banks
(AFB), is reviewing the employee training programs of AFB banks. His
staff randomly selected personnel files for 10 tellers in the Southwest
Region, and determined that their mean training time was 25 hours and
that the standard deviation was 5 hours. Assume that training times are
normally distributed. The 95% confidence interval for the population
variance of training times is (9) .
Tamara Hill, fund manager of the Hill Value Fund, manages a portfolio of
250 common stocks. Tamara is searching for a ‘low risk’ issue to add to the
portfolio, i.e., one with a price variance less than that of the S&P 500 index.
Moreover, she assumes an issue is not ‘low risk’ until demonstrated
otherwise. Her staff reported that during the last nine quarters the price
variance for the S&P 500 index (population 1) was 25, and for the last
seven quarters the price variance for XYC common (population 2) was 6.
Assume that stock prices are normally distributed in the population. Using
α = 0.05 , the observed F value is (10) .
A store manager wishes to determine whether his customers would be
prepared to pay a little extra for organic produce. He uses a random
number table to choose 50 random numbers between 1 and 200. He stands
outside the store on a Monday morning between 9:00 a.m. and 12:00 noon
and interviews the people corresponding to the random numbers. For
example random number 82 would correspond to the 82nd person to arrive.
Do you think that the sample obtained in this way will be representative of
all the store’s customers? (10%)
6.2% of VCRs of a certain type are defective. Let the random variable X
represent the number of defective VCRs among 200 randomly selected
VCRs of this type. Suppose you wish to find the probability that X is equal
to 8.
A) Does the random variable X have a binomial or a Poisson distribution?
How can you tell? (5%)
B) If X has a binomial distribution, would it be reasonable to use the
Poisson approximation? If not, why not? (5%)
Suppose that we want to decide whether a newly developed gasoline
additive increases gas mileage. 10 cars are selected at random and that the
cars sampled are driven both with and without the additive, yielding a
paired sample of size 10. Further suppose that the resulting gas mileages,
in miles per gallon (mpg), are as displayed in the second and third columns
of the following Table. At the 5% significance level, do the data provide
sufficient evidence to conclude that, on average, the gasoline additive
improves gas mileage?
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