Download 1 - JustAnswer

1. In a manufacturing process a random sample of 36 bolts manufactured has a mean of 3 inches w/ a
standard deviation of .3 inches. What is the 99% confidence interval for the true mean length of the bolt?
Confidence interval =
= (2.87, 3.13)
2. When the population is normally distributed, population standard deviation σ is unknown, and the
sample size is n = 15; the confidence interval for the population mean σ is based on the ________.
Sample standard deviation, s.
3. Suppose that the percentage returns for a given year for all stocks listed on the NYSE are approximately
normally distributed with a mean of 12.4 % & a standard deviation of 20.6%. Consider drawing a random
sample of n = 5 stocks from the population of all stocks and calculating the mean return, x-bar of the
sampled stocks. Find the mean and the standard deviation of the sampling distribution of x-bar, and find an
interval containing 95.44% of all possible sample mean returns.
Mean = 12.4
Standard deviation =
Interval =
= (-6.03, 30.83)
4. A study asked parents who own TVS equipped with V-chips whether they use the devices to block
programs with objectionable content. a) Suppose that we wish to use the study results to justify the claim
that fewer than 20% of parents who own TV sets with V-chips use the devices. The study actually found
that 17% of the parents polled used their V-chips. If the poll surveyed 1,000 parents, and if for the sake of
argument we assume that 20% of parents who own V-chips actually use the devices (that is, p - = .2),
calculate the probability of observing a sample portion of .17 or less. That is, calculate P(p ≤ .17). b) Based
on the probability you computed in part a, would you conclude that fewer than 20% of parents who won
TV sets equipped with V-chips actually use the devices? Explain.
a.
P(p ≤ .17) = P(z ≤
) = P(z ≤ -2.3717) = 0.0089
b.
No. The probability is very small.
5. Suppose that an independent laboratory has tested trash bags and found that no 30-gal. bags that are
currently on the market have a mean breaking strength of 50 lbs or more. On the basis of these results, the
producer of the new, improved trash bag feels sure that its 30-gal. bag will be the strongest such bag on the
market if the new trash bag’s mean breaking strength can be shown to be at least 50 lbs. The mean of the
sample of 40 trash bag breaking strengths in Table 1.9 is x-bar = 50.575. If we let μ denote the mean of the
breaking strengths of all possible trash bags of the new type and assume that σ equals 1.65: a) Calculate
95% and 99% confidence intervals for μ. b) Using the 95% confidence interval, can we be 95% confident
that μ is at least 50 lbs? Explain. c) Using the 99% confidence interval, can we be 99% confident that μ is at
least 50 lbs? Explain. d) Based on your answers to parts b and c, how convince are you that the new 30-gal.
trash bag is the strongest such bag on the market?
a)
95% confidence interval =
99% confidence interval =
= (50.064, 51.086)
= (49.903, 51.247)
b) Using 95% confidence we can conclude that μ is at least 50 lbs. Confidence interval is all above
50 lbs.
c) Using 99% confidence we can not conclude that μ is at least 50 lbs. Confidence interval is not all
above 50 lbs. It is somewhere in between the two limits.
d) We are only 95% confident that it is the strongest such bag on the market.
6. Quality Progress, February 2005, reports on the results achieved by Bank of America (BoA) in
improving customer satisfaction and customer loyalty by listening to the “voice of the customers.” A key
measure of customer satisfaction is the response on a scale from 1 to 10 to the question: “Considering all
the business you do with BoA, what is your overall satisfaction with BoA?” Suppose that a random sample
of 350 current customers results in 195 customers with a response of 9 or 10 representing “customer
delight.” Find a 95% confidence interval for the true proportion of all current BoA customers who would
respond with a 9 ro 10. Are we 95% confident that this proportion exceeds.48, the historical proportion of
customer delight for BoA?
Confidence interval =
= (0.505, 0.609)
Yes, we are 95% confident that the proportion exceeds .48 because the confidence
interval is all over .48.