# STATS

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1-Suppose that the fuel comsumption of cars for the same model is normally distributed. A random sample
of ten new cars of the same model are randomly selected and their fuel consumption (l/100 km) is
determined by subjecting them to a road test of 500 km. Their mean fuel consumption is 7.97 (l/100 km)
and their variance fuel consumption is 8.10(l/100 km). The standard error of the sample mean is
(1) 2.521
(2) 0.285
(3) 1.111
(4) 0.810
(5) 0.90

2-A manufacturing company packages peanuts for Piedmont Airlines. The individual packages weigh 1.4
grams with a standard deviation of 0.6 grams. For a flight of 152 passengers receiving the peanuts, the
probability that the average weight of the packages is less than 1.3 grams is
(1) 0.0202
(2) 0.2040
(3) 0.9798
(4) 0.4798
(5) 2.0500

3-The proportion of coaches who spend more than 120 minutes at the sport is 0.023.
Out of 1000 coaches, the expected number who will spend more than 120 minutes at the sport is:
(1) 1023
(2) 120000
(3) 23
(4) 977
(5) 63.24

4-Consider an infinite population with a mean of 160 and a standard deviation of 25. A random sample of
size 64 is taken from this population.
The standard deviation of the sample mean equals:
(1) 12.649
(2) 25.000
(3) 2.560
(4) 3.125
(5) 0.391

5-The following five statements refer to using the t-table in the correct way for a given probability. However,
one statement is incorrect. Find the incorrect statement.
(1) For 25 degrees of freedom, the value of A that corresponds to P (t ¡Ý A) = 0.025 is A = 2.060
(2) For 25 degrees of freedom, the value of A that corresponds to P (t ¡Ü A) = 0.10 is A = −1.316
(3) For 25 degrees of freedom, the value of A that corresponds to P (−A ¡Ü t ¡Ü A) = 0.99 is A = 2.787
(4) For 85 degrees of freedom, the value of A that corresponds to P (t ¡Ü A) = 0.025 is A = 1.988
(5) For 85 degrees of freedom, the value of A that corresponds to P (−A ¡Ü t ¡Ü A) = 0.98 is A = 2.371

6-A random sample of 30 women drank an average of 15 cups of coffee per week during examination finals,
with the sample standard deviation equal to 3 cups. A upper limit of an approximate confidence interval
with 95% of the population average cup drunk is
(1) 15.000
(2) 13.9265
(3) 16.1201
(4) 1.60735
(5) 16.0735

7-A statistics practitioner wishes to test the following hypothesis: H0 : ¦Ì = 600 against H1 : ¦Ì < 600
A sample of 50 observations yielded the statistics: mean x = 585 and standard deviation sx = 45. The
test statistic of a test to determine whether there is enough evidence at the 10% significance level to reject
the null hypothesis is
(1) 2.3570
(2) 0.3333
(3) 16.6667
(4) 23.570
(5) −2.3570