Download Review for the Final

Review for the Final Exam
I. Below are the times between eruptions of the Old Faithful Geyser, find the mean, median, mode, range,
variance and standard deviation for the data:
98, 92, 95, 87, 96, 90, 65, 92, 95, 93, 98, 94
II. A city assessor wished to estimate the mean income per household. The previous mean income was
$25,300. A random sample of 12 households in the city showed a mean income of $29,400 and a standard
deviation of $6325.
(a) Find a 95% confidence interval for  , the population mean income per household in the city.
(b) Based on your answer in part (a), would the assessor conclude that the mean income had increased over the
previous estimate of $25,300?
III. . A study was recently done that emphasized the problem we all face with drinking and driving. Four
hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of
vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:
Number of Vehicles Involved
a) What proportion of the accidents involved a single car without the effect of alcohol?
b) What proportion involved No alcohol or a single car?
c) Assuming No alcohol involvement, what proportion of the accidents involved a single car?
d) What proportion of the accidents involved more than a single vehicle?
e) What proportion involved alcohol or a single car?
IV. The Aid to Families with Dependent Children program has an overall error rate of 4% in determining
eligibility. The state of California uses sampling to monitor its counties to see whether they exceed the 4%
error rate, which can result in economic sanctions. In one county, 9 cases out of 150 were found to be in error.
(a) Find a 98% confidence interval for the error rate for the county (proportion of all cases in error).
(b) Based on your answer in part (a), would you conclude that the error rate is above the 4% rate?
V. Current estimates suggest that only 60% of the home-based computers have access to on-line services.
Suppose 25 people with home-based computers were randomly and independently sampled.
 Find the probability that at least 10 but at most 14 currently have access to on-line services.
 Find the probability that less than quarter of those sampled currently have no access to on-line services.
 Find the probability that at least 18 currently have access to on-line services.
 How many people do you expect currently do not have access to on-line services?
VI. The weight of corn chips dispensed into a 10-ounce bag by the dispensing machine has been identified as
possessing a normal distribution with a mean of 10.5 ounces and a standard deviation of .2 ounces. Suppose
100 bags of chips were randomly selected from this dispensing machine. Find the probability that the sample
mean weight of these 100 bags exceeded 10.45 ounces.
VII. Last year the average daily change in the Dow Jones Industrial Index was 7.3 points. A random sample of
15 trading days this year showed the average change to be 5.2 points with standard deviation 10.2. Test the
claim that the average change in the index is less this year than it was last year. Use a 5% significance level.
VIII. In one Pepsi television commercial, an announcer states that ``in recent blind taste tests, more than half the
Diet Coke drinkers surveyed said they preferred the taste of Diet Pepsi'' Suppose 100 Diet Coke drinkers took the
Pepsi Challenge and 56 preferred the taste of Diet Pepsi. Test the hypothesis that more than half of all Diet Coke
drinkers will select Diet Pepsi in the blind taste test. Use  =.05.
IX. Complete each sentence by putting an appropriate word, phrase or symbol in each blank.
1) If the median of a population is smaller than its mean, then the population is skewed to the __________
2) For any distribution,
___ % of the observations will lie within three standard deviations of its mean.
3) If the random variable X is binomial with n = 100 and p = .72, then the mean = ,
4) If you reject the null hypothesis when it is true, you make a Type ______
5) If the events A and B are mutually exclusive, P(AB) =
6) If the P-value of the test statistic is
and variance =
error.
.
________ than α, fail to reject the null hypothesis.
7) If the null hypothesis, Ho is  = 175, then the research hypothesis, Ha is:  ____
8) If the test statistic is z and α = .10, then the rejection region for a two-tailed test is : __________
X. The length of time it takes college students to find a parking spot in the library parking lot follows
a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute. Find the
probability that a randomly selected college student will take between 3.0 and 4.5 minutes to find a
parking spot in the library lot.
XI. The tread life of a particular brand of tire is a random variable best described by a normal
distribution with a mean of 60,000 miles and a standard deviation of 2200 miles. What warranty
should the company use if they want 96% of the tires to outlast the warranty?
XII. A statistics class consists of 24 students who are either unemployed or who are working in low-paying
part-time jobs. The class also includes a professor who is paid an enormous salary (I wish!). Would it be
better to use the mean, median, or the mode to describe the earnings of the typical person in the class of 25
people?
XIII. The average of a set of data points is 13.5, and the median of the same data set is 8.2. Is the distribution
skewed? If so, is it right or left skewed?