1 An engineer is investigating the strength of a new type of

1- An engineer is investigating the strength of a new type of fastener. The only information she has right now is that the strength of a similar fastener has a standard deviation of 35. Assuming that the new fasteners have the same standard deviation, how many fasteners should she test so that she can be 99% confident that the sample mean will be within ± 10 of the true mean strength?

15

30

50

82

2- A random sample of 100 people was taken.  Eighty of the people in the sample favored Candidate

A.  The 95% confidence interval for the true proportion of people who favors Candidate A is

0.722 to 0.878

0.762 to 0.838

78.04 to 81.96

62.469 to 97.531

3-A sample is taken to determine the average time (in minutes) spent waiting to get on rides at an amusement park. A 95% confidence interval for the population mean is (3.8, 4.4). Which of the following is the correct interpretation of this interval?

There is a 95% probability that the population mean lies in the interval (3.8, 4.4).

95% of the people will wait between 3.8 minutes and 4.4 minutes to get on a ride.

We can be 95% confident that the interval (3.8, 4.4) contains the population mean.

On 95% of the days, the average waiting time is between 3.8 minutes and 4.4 minutes.

Solution

Q1.
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.01% LOS is = 2.58 ( From Standard Normal Table )
Standard Deviation ( S.D) = 35
ME =10
n = ( 2.58*35/10) ^2
= (90.3/10 ) ^2
= 81.541 ~ 82      

Q2.
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=80
Sample Size(n)=100
Sample proportion = x/n =0.8
Confidence Interval = [ 0.8 ±Z a/2 ( Sqrt ( 0.8*0.2) /100)]
= [ 0.8 - 1.96* Sqrt(0.0016) , 0.8 + 1.96* Sqrt(0.0016) ]
= [ 0.726,0.878]

Q3.
We can be 95% confident that the interval (3.8, 4.4) contains the population mean.