Confidence Interval and Statistical Analysis

6. A producer of a juice drink advertises that it contains 10% real
fruit juices. A sample of 75 bottles of the drink is analyzed and the
percent of real fruit juices is found to be 6.5%. If the true
proportion is actually .10, what is the probability that the sample
percent will be 6.5% or less? Based on the sample, what would you
conclude about the juice producers’ claims of “…contains 10% real
fruit juices…�?

7. The security department of a state university is planning its budget
for the next year. In estimating the man-hours for security during
university sponsored music concerts, the average length of music
concerts is needed. A random sample for 36 security departments at
universities was taken and the sample mean length of concerts was 160
minutes. Suppose the standard deviation is 45 minutes. Prepare an 84
percent confidence interval for the true mean duration of music
concerts.

8. A bank holds the mortgage on a motel that the motel owner says has
an average daily revenue of $2048. In the event the average is not at
least $2048, the bank will ask the motel owner for additional collateral
for the loan as protection against loan default. A loan officer is
aware that the daily average revenue is normally distributed and
randomly selects 20 days during the last six months. The sample has a
mean of $2003 and standard deviation of $144. Based on an appropriate
statistical analysis and the sample taken by the loan office, determine
whether the bank should ask for additional collateral.

9. The tourist bureau of a large populous state is concerned about the
motel space available for holding a world’s fair. Previous occupancy
rates have been 60%. In order to determine whether any change in the
occupancy rate has occurred the bureau takes a random survey of 500
motels in the state. The reported occupancy rate of these 500 motels is
65%. Based on the sample taken, and an appropriate statistical
analysis, determine the maximum level of confidence at which it can be
said that the occupancy rates are not as believed to be previously.

10. A long-haul truck drive is eligible for a year-end bonus if the
average miles driven per day are more than 375 miles per eight-hour day.
To determine whether or not a drive is to receive a year-end bonus, a
random sample of 36 days from the driver’s logbook is taken and the
sample mean of 405 miles and standard deviation of 70 is computed. What
is the maximum level of confidence at which it can be said that this
driver is eligible for a bonus?