Question 1:
A random sample of 18 young adult men (2030 years old) was taken. Each man was asked how many
minutes of sports they watched on television daily. It is known that the STD = 10. Test to determine at the
5% significance level whether there is enough statistical evidence to infer that the mean amount of
television watched daily by all young adult men is greater than 50 minutes?
ZTest: Mean
Mean
59.166
7
Standard Deviation
9.9425
Observations
18
Hypothesized Mean
1
SIGMA
10
z Stat
24.678
P(Z<=z) onetail
0
z Critical onetail
1.6449
P(Z<=z) twotail
0
z Critical twotail
1.96
Yes, there is enough statistical evidence to infer that the mean mount of television watched daily by
young men is greater than 50 minutes.
Question 2:
A statistics practitioner would like to estimate a population mean to within 50 units with 99% confidence
given that the population standard deviation is 250.
^ = exponent
A)
What sample size should be used?
n = (2.576^2 * 250^2)/50^2
n = (6.636* 62500)/2500
n = 165.89 which rounds up to a sample size of 166
(Rounding up) n = 166
B)
Repeat part (a) with a standard deviation of 50:
n = (z^2 * σ^2)/c^2
n = (2.576^2 * 50^2)/50^2
n = (6.636* 2500)/2500
n = 6.64
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(Rounding up) n = 7
C)
Repeat part (a) using a 95% confidence level:
n = (z^2 * σ^2)/c^2
n = (1.96^2 * 250^2)/50^2
n = (3.842* 62500)/2500
n = 96.04
(Rounding up) n = 97
D)
Repeat part (a) when we wish to estimate the population mean to within 10 units:
n = (z^2 * σ^2)/c^2
n = (2.576^2 * 250^2)/10^2
n = (6.636* 62500)/100
n = 4147.36
(Rounding up) n = 4148
Question 3:
Some traffic experts believe that the major cause of highway collisions in the differing speeds of cards.
That is when some cars are driven slowly while others are driven at speeds well in excess of the speed
limit, cars tend to congregate in bunches, increasing the probability of accidents. Thus the greater the
variation in speeds, the greater will be the number of collisions that occur. Suppose that one expert
believes that when the variance exceeds 18mph, the number of accidents will be unacceptably high. A
random sample of the speeds of 245 cars on a highway with one of the highest accident rates in the
country is taken. Can we conclude at the 10% significance level that the variance in speeds exceeds
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 Summer '11
 Sukar
 Normal Distribution, Standard Deviation, Variance, Operations Manager

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