- (15 pts) In Summer 2004, a random sample of 128 Sitka residents was
conducted to gain insight into the level of local interest in a
long-range visitor industry plan for Sitka. Of the 128 survery
respondents, 29 identified themselves as business owners. The
following questions are based on the survey results.
- When asked whether there is a need for Sitka to develop a long-range
visitor industry plan, 102 of the 128 respondents said yes. Calculate the
z-score for this result under the null hypothesis that 50% of the population
is in favor of a long term plan. Is it justifiable to conclude that a majority of
Sitkans are in favor of a long term plan? Explain.
- Surveys were conducted via telephone. Suppose that as part of the
introduction those surveyed were told, "due to widespread interest in a long-term
plan for managing the tourism industry, the visitor industry study group was formed
to begin looking at the issues." Do you think this would introduction would
introduce no bias, a bias high, or a bias low for the survey question addressed in
part a? Explain.
- When asked about multiple day visitors and maintaining or improving quality of
life 39 of 99 non-business owners said that an increase in the number of multiple
day visitors would help. When asked the same question 19 of the 29 business owners
responded that an increase in the number of multiple day visitors would be
beneficial. Construct a 95% confidence interval for pnb - pb.
What can you conclude about the difference between the proportion
of non-business owners who think increased multiple day visitors is beneficial
(pnb) and the proportion of business owners who think that
(pb)? Explain.
- (20 pts) Suppose that for the Indian River stock of coho salmon the distribution
of the weights of returning adult males has a mean μ=9.5 lbs with a standard
deviation σ=.55.
- If a biologist randomly selects 25 different returning Indian River males and
weighs them what will the approximate distribution of the sample mean,
x be?
- If the biologist selected 100 fish would you expect
x to be closer to or further from 9.5?
Explain.
- It is suspected that the Nawkwasina stock of coho salmon tend to
be larger than the Indian River stock, so a biologist decides
to randomly select 100 fish from the returning Nawkwasina adults and do a
hypothesis test to check. State the null and alternative
hypotheses.
- If the biologist found a sample mean x=9.65 lbs and
the sample standard deviation s=.70, what is the p-value for this result? Is it
significant at the α=.05 level? What should the biologist conclude?
- (10 pts) Give two sources of error that are not accounted for in the
z-procedures of Chapter 13 and 14 and briefly explain how they may
affect results.
- (5 pts) Suppose a researcher conducts a hypothesis test with the null hypothesis
H0: μ=0 and alternative Ha:μ>0. Consider two cases,
one where the true value was actually μ=.5 and the other μ=2.5. All else being
equal, in which case would the researcher be more likely to make a Type II error?
Explain.
- (5 pts) While reading a journal article, you see that the
researcher has computed a 95% confidence interval for the mean weight
loss of patients undergoing a certain cancer treatment. The interval
is (1.1, 4). What does this mean?
- (5 pts) An industrial researcher conducted a pilot study and found
the standard deviation of the production item length to be
approximately 0.7 mm. If the researcher desires to obtain an estimate
for the true mean length that is within .05mm (with 95% confidence),
what is the approximate sample size that should be used?