QA 233 (Basic
Business Statistics)
Practice Problems
VIII
- Chapters 7 & 8
- When
surveyed, 41 out of 200 respondents indicate that ‘Twinkies’ are their
favorite snack food. Provide both a point estimate and an interval estimate
(at the 92% level of confidence) of the share of the population for whom
‘Twinkies’ are their favorite snack food. At the 90% level of
confidence, what is the margin of error?
- Suppose
that the mean sales for nineteen randomly selected restaurants in the
‘Hamburger Haven’ chain (which consists of 800 restaurants) during the
week of the Thanksgiving holiday are $9,250.00. If the standard deviation of
these sample results is $1250.00, what is the 95% confidence interval?
- Suppose
that the mean sales for nineteen randomly selected restaurants in the
‘Hamburger Haven’ chain (which consists of 800 restaurants) during the
week of the Thanksgiving holiday are $9,250.00. If the standard deviation of
these sample results is $1250.00 and mean weekly sales for restaurants in
the ‘Hamburger Haven’ chain tends to be normally distributed, what is
the 95% confidence interval?
- If
the actual mean weekly sales restaurants in the ‘Hamburger Haven’ chain
is $11,200.50 and the actual standard deviation of weekly sales for
restaurants in the ‘Hamburger Haven’ chain is $2,898.43, what is the
probability that a randomly selected sample of 43 restaurants in the
‘Hamburger Haven’ will yield a mean of $12,500.00 or greater? Under
these conditions, what is the probability that a randomly selected sample of
43 restaurants in the ‘Hamburger Haven’ will yield a mean between
$12,000.00 and $12,230.00?
- If
5% of all output produced by a machine is defective, what is the probability
that the proportion of defectives in the output produced by the machine
today (300 units) is between .04 and .07? If our policy is perform
maintenance on the machine when the proportion of defects in one day’s
production exceeds 0.06, what is the probability that we will have to call
maintenance at the end of any day? Given your results, what do you think of
their maintenance policy (to perform maintenance on the machine when the
proportion of defects in one day’s production exceeds 0.06)?
- Suppose
that the mean checking account balance at a local bank is $750.00, and the
standard deviation of checking account balances at the local bank is
$500.00. Construct an interval that will contain 90% of all possible sample
mean checking account balances that can result from a random sample of 45
checking accounts taken from the local bank.
- Farmer
Douglass, who has an orchard of 2,000 pomegranate trees, wants to estimate
the proportion of trees whose fruit are ripe. He and his able bodied
assistant Eb randomly select 35 trees and determine that the fruit of 19 of
the sampled trees is ripe. Farmer Douglass now wants an interval estimate,
at the 99% confidence level, of the proportion of trees in his orchard whose
fruit are ripe. Please provide farmer Douglass with this estimate. Do you
think that this interval estimate will be useful to farmer Douglass? Why or
why not?
- Suppose
that 82% of all investors in the bond market earned a profit during the past
fiscal year. Local bond dealer E. Z. Cash has seventy investors in the bond
market, fifty of whom earned a profit during the past fiscal year.
If we randomly select seventy investors, what is the probability the
proportion of these investors who earned a profit during the past fiscal
year would be at least as low as the proportion of E. Z.’s investors who
earned a profit during the past fiscal year?
- A
computer equipment manufacturer advertises that their 2500-L laser jet
printer averages 12 printed pages per minute with a standard deviation of
1.50 pages per minute. You randomly select 50 documents from your hard drive
and measure the number of pages printed in the first minute of printing for
each document. The mean number of pages printed in the first minute for
these 50 documents is 11.4. If the advertisement is accurate, what is the
probability of getting results at least as poor as those you obtained (i.e.,
that the print speed is no more than 11.4 pages per minute for the first
minute of printing for 50 randomly selected documents)?
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